IB 12

1

Particle Mass Electric Charge

Electron me = 9110 x 10-31 kg q = -eq = -160 x 10-19 C

Proton mp = 1673 x 10-27 kg q = +eq = +160 x 10-19 C

Neutron mn = 1675 x 10-27 kg q = 0q = 0 C

Electrostatics1) electric charge 2 types of electric charge positive and negative

2) charging by friction transfer of electrons from one object to another

3) positive object lack of electrons negative object excess of electrons

Conservation of Electric Charge The total electric charge of an isolated system remains constant

4) Types of materials

a) Conductors materials in which electric charges move freely (eg metals graphite)

b) Insulators materials in which electric charges do not move freely (eg plastic rubber dry wood glass ceramic)

c) Semiconductors materials with electrical properties between those of conductors and insulators (eg silicon)

d) Superconductors materials in which electrical charges move without resistance (eg some ceramics at very low temperatures)

Properties of Atomic Particles

e = elementary unit of charge (magnitude of charge on electron)

e = 160 x 10-19 C

DO 1 A balloon has gained 2500 electrons after being rubbed with wool What is the charge on the balloon What is the charge on the wool

DO 2 A rubber rod acquires a charge of -45 μC How many excess electrons does this represent

IB 12

2

Electric Force (Electrostatic Force Coulomb Force)

Coulombrsquos Law The electric force between two point charges is directly proportional to the product of the two charges and inversely proportional to square of the distance between them and directed along the line joining the two charges

NOTE +-F denotes direction of force not sign of charge

k = Coulomb constant (electrostatic constant)

k = 899 x 109 Nm2 C -2

k = 1 4πε0

ε0 = permittivity of free space = 885 x 10-12 C2 N-1 m -2

Coulomb Force

Point charge a charged object that acts as if all its charge is concentrated at a single point

Alternate formula for Coulomb force

DO Use the Coulomb force to estimate the speed of the electron in a hydrogen atom

IB 12

3

The Principle of Superposition

The net electric force acting on a charged particle is the vector sum of all the electric forces acting on it

DO 1 Determine the net electrostatic force on charge q1 as shown below

DO 2 Where can a third charge of +10 microC be placed so that the net force acting on it is zero

DO 3 Three point charges of -20 microC are arranged as shown Determine the magnitude and direction of the net force on charge q1

IB 12

4

Electric Field

Electric field a region in space surrounding a charged object in which a second charged object experiences an electric force

Test charge a small positive charge used to test an electric field

Electric Field Diagrams (DO ALL 7)1 Positively charged sphere 2 Positive point charge 3 Negative point charge

Radial Field field lines are extensions of radii

4 Two positive charges 5 Two negative charges 6 Two unlike charges

Properties of Electric Field Lines

1 Never cross

2 Show the direction of force on a small positive test charge

3 Out of positive into negative

4 Direction of electric field is tangent to the field lines

5 Density of field lines is proportional to field strength (density = intensity)

6 Perpendicular to surface

7 Most intense near sharp points

7 Oppositely charged parallel plates

Edge Effect bowing of field lines at edges

Uniform Field field has same intensity at all spots

IB 12

5

Electric Field Strength (Intensity) electric force exerted per unit charge on a small positive test charge

Electric Field Strength

Units NC

Electric Field Electric Field for a Point Charge

Point Charge Spherical Conductor

DO 1 a) Find the magnitude and direction of the electric field at a spot 0028 meter away from a sphere whose charge is +354 microcoulombs and whose radius is 060 centimeters

b) Find the magnitude and direction of the electric force acting on a -702 nC charge placed at this spot

c) Find the electric field strength at the surface of the sphere

DO 2 a) Find the magnitude and direction of the gravitational field at an altitude of 100 km above the surface of the Earth

b) Find the magnitude and direction of the gravitational force exerted on a 60 kg bowling ball placed at this spot

c) Find the gravitational field strength at the surface of the Earth

Electric Force

Units N

IB 12

6

DO 3 a) Find the magnitude and direction of the net electric field halfway between the two charges shown below

b) Determine the electric force on a proton placed at this spot

DO 4 Two charged objects A and B each contribute as follows to the net electric field at point P EA = 300 NC directed to the right

and EB = 200 NC directed downward What is the net electric field at P

DO 5 a) Two positive point charges q1 = +16 C and q2 = +40 C are separated in a vacuum by a distance of 30 m Find the

spot on the line between the charges where the net electric field is zero

IB 12

7

DO 6 A proton is released from rest near the positive plate The distance between the plates is 30 mm and the strength of the electric field is 40 x 103 NC

a) Describe the motion of the proton

b) Write an expression for the acceleration of the proton

c) Find the time it takes the proton to reach the negative plate d) Find the speed of the proton when it reaches the negative plate

DO 7 A particle is shot with an initial speed through the two parallel plates as shown

a) Sketch and describe the path it will take if it is a proton an electron or a neutron

b) Which particle will experience a greater force

c) Which particle will experience a greater acceleration

d) Which particle will experience a greater displacement

DO 8 In the figure an electron enters the lower left side of a parallel plate capacitor and exits at the upper right side The initial speed of the electron is 550times106 ms The plates are 350 cm long and are separated by 0450 cm Assume that the electric field between the plates is uniform everywhere and find its magnitude

IB 12

8

Electric Potential Energy

Gravitational Potential Energy (EP)

Base level where EP = 0

High amount of EP

Low amount of EP

Reason for EP

1 Test object has mass (test mass = m)

2 Test mass is in a gravitational field (g) caused by larger object (M)

3 Larger object exerts a gravitational force on test mass (Fg = mg)

4 Test mass has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Gravitational potential energyEP = mgh W = ΔEP = mg Δh

Electric Potential Energy (EP)

High amount of EP

Low amount of EP

Reason for EP

1 Test object has charge (test charge = +q)

2 Test charge is in an electric field caused by larger object (Q)

3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Electric potential energyEP = Eq hW = ΔEP = Eq Δh

Base level where EP = 0

Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field

EP = 0(Work done by field)

Derivation for Point Charges

Electric Potential Energy due to a point charge

Formula Units

J

Type

scalar

IB 12

9

Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field

Electric Potential due to a point charge

Formula

Units

JC= volts(V)

Type

scalar

ABHigher potential Lower potential

Zero potential

AB

Lower potential Higher potentialZero potential

DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge

b) How much potential energy will an electron have if it is at this spot

c What is the potential where a proton is placed 096 m from a -12 nC charge

IB 12

10

Point Charges

+Q +Q +Q +Q

Electric Force Electric Field Electric Potential Energy Electric Potential

Two objects needed ndash interaction between the two

Magnitude F = Eq

F = kQqr2

Units N

Type vector

Direction likes repel unlikes attract

Sign donrsquot use when calculating ndash check frame of reference

One object needed ndash property of the field

Magnitude V = EPq

V = kQr

Units JC

Type scalar (+-)

Sign use sign of Q

Two objects needed ndash quantity possessed by the system

Magnitude EP = qV

EP = kQqr

Units J

Type scalar (+-)

Sign use signs of Q and q

One object needed ndash property of that one object

Magnitude E = Fq

E = kQr2

Units NC

Type vector

Direction away from positive towards negative

Sign donrsquot use when calculating ndash check frame of reference

F = 0 where E = 0 EP = 0 where V = 0

IB 12

11

DO 1 a) Calculate the net electric field at each spot (A and B)

b) Calculate the net electric force on a proton placed at each spot

DO 2 a) Calculate the net electric potential at each spot (A and B)

b) Calculate the electric potential energy of a proton placed at each spot

IB 12

12

Electric Potential and Conductors

For a hollow or solid conductor

1 all the charge resides on the outside surface

2 the electric field is zero everywhere within

3 the external electric field acts as if all the charge is concentrated at the center

4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance

Elec

tric

Fiel

d St

reng

th

Value at surface = kQr2

radius

Graphs for a spherical conductor

Distance

Elec

tric

Pote

ntia

l

radius

DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC

a) What is the electric field at the center of the sphere

b) What is the electric field at the surface of the sphere

c) What is the electric field at a distance of 075 m from the surface of the sphere

d) What is the electric potential at the surface of the sphere

e) What is the electric potential at the center of the sphere

f) What is the electric potential at a distance of 075 m from the surface of the sphere

IB 12

13

Equipotential Surfaces

Equipotential surface a surface on which the electric potential is the same everywhere

1 Locate points that are at the same electric potential around each of the point charges shown

2 Sketch in the electric field lines for each point charge

3 What is the relationship between the electric field lines and the equipotential surfaces

PerpendicularField lines point in direction

of decreasing potential

Electric Potential Gradient

The electric field strength is the negative of the electric potential gradient

Formula

Units Nc or Vm

For each electric field shown sketch in equipotential surfaces

Sketch in equipotential surfaces for the two configurations of point charges below

httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html

IB 12

2

Electric Force (Electrostatic Force Coulomb Force)

Coulombrsquos Law The electric force between two point charges is directly proportional to the product of the two charges and inversely proportional to square of the distance between them and directed along the line joining the two charges

NOTE +-F denotes direction of force not sign of charge

k = Coulomb constant (electrostatic constant)

k = 899 x 109 Nm2 C -2

k = 1 4πε0

ε0 = permittivity of free space = 885 x 10-12 C2 N-1 m -2

Coulomb Force

Point charge a charged object that acts as if all its charge is concentrated at a single point

Alternate formula for Coulomb force

DO Use the Coulomb force to estimate the speed of the electron in a hydrogen atom

IB 12

3

The Principle of Superposition

The net electric force acting on a charged particle is the vector sum of all the electric forces acting on it

DO 1 Determine the net electrostatic force on charge q1 as shown below

DO 2 Where can a third charge of +10 microC be placed so that the net force acting on it is zero

DO 3 Three point charges of -20 microC are arranged as shown Determine the magnitude and direction of the net force on charge q1

IB 12

4

Electric Field

Electric field a region in space surrounding a charged object in which a second charged object experiences an electric force

Test charge a small positive charge used to test an electric field

Electric Field Diagrams (DO ALL 7)1 Positively charged sphere 2 Positive point charge 3 Negative point charge

Radial Field field lines are extensions of radii

4 Two positive charges 5 Two negative charges 6 Two unlike charges

Properties of Electric Field Lines

1 Never cross

2 Show the direction of force on a small positive test charge

3 Out of positive into negative

4 Direction of electric field is tangent to the field lines

5 Density of field lines is proportional to field strength (density = intensity)

6 Perpendicular to surface

7 Most intense near sharp points

7 Oppositely charged parallel plates

Edge Effect bowing of field lines at edges

Uniform Field field has same intensity at all spots

IB 12

5

Electric Field Strength (Intensity) electric force exerted per unit charge on a small positive test charge

Electric Field Strength

Units NC

Electric Field Electric Field for a Point Charge

Point Charge Spherical Conductor

DO 1 a) Find the magnitude and direction of the electric field at a spot 0028 meter away from a sphere whose charge is +354 microcoulombs and whose radius is 060 centimeters

b) Find the magnitude and direction of the electric force acting on a -702 nC charge placed at this spot

c) Find the electric field strength at the surface of the sphere

DO 2 a) Find the magnitude and direction of the gravitational field at an altitude of 100 km above the surface of the Earth

b) Find the magnitude and direction of the gravitational force exerted on a 60 kg bowling ball placed at this spot

c) Find the gravitational field strength at the surface of the Earth

Electric Force

Units N

IB 12

6

DO 3 a) Find the magnitude and direction of the net electric field halfway between the two charges shown below

b) Determine the electric force on a proton placed at this spot

DO 4 Two charged objects A and B each contribute as follows to the net electric field at point P EA = 300 NC directed to the right

and EB = 200 NC directed downward What is the net electric field at P

DO 5 a) Two positive point charges q1 = +16 C and q2 = +40 C are separated in a vacuum by a distance of 30 m Find the

spot on the line between the charges where the net electric field is zero

IB 12

7

DO 6 A proton is released from rest near the positive plate The distance between the plates is 30 mm and the strength of the electric field is 40 x 103 NC

a) Describe the motion of the proton

b) Write an expression for the acceleration of the proton

c) Find the time it takes the proton to reach the negative plate d) Find the speed of the proton when it reaches the negative plate

DO 7 A particle is shot with an initial speed through the two parallel plates as shown

a) Sketch and describe the path it will take if it is a proton an electron or a neutron

b) Which particle will experience a greater force

c) Which particle will experience a greater acceleration

d) Which particle will experience a greater displacement

DO 8 In the figure an electron enters the lower left side of a parallel plate capacitor and exits at the upper right side The initial speed of the electron is 550times106 ms The plates are 350 cm long and are separated by 0450 cm Assume that the electric field between the plates is uniform everywhere and find its magnitude

IB 12

8

Electric Potential Energy

Gravitational Potential Energy (EP)

Base level where EP = 0

High amount of EP

Low amount of EP

Reason for EP

1 Test object has mass (test mass = m)

2 Test mass is in a gravitational field (g) caused by larger object (M)

3 Larger object exerts a gravitational force on test mass (Fg = mg)

4 Test mass has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Gravitational potential energyEP = mgh W = ΔEP = mg Δh

Electric Potential Energy (EP)

High amount of EP

Low amount of EP

Reason for EP

1 Test object has charge (test charge = +q)

2 Test charge is in an electric field caused by larger object (Q)

3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Electric potential energyEP = Eq hW = ΔEP = Eq Δh

Base level where EP = 0

Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field

EP = 0(Work done by field)

Derivation for Point Charges

Electric Potential Energy due to a point charge

Formula Units

J

Type

scalar

IB 12

9

Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field

Electric Potential due to a point charge

Formula

Units

JC= volts(V)

Type

scalar

ABHigher potential Lower potential

Zero potential

AB

Lower potential Higher potentialZero potential

DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge

b) How much potential energy will an electron have if it is at this spot

c What is the potential where a proton is placed 096 m from a -12 nC charge

IB 12

10

Point Charges

+Q +Q +Q +Q

Electric Force Electric Field Electric Potential Energy Electric Potential

Two objects needed ndash interaction between the two

Magnitude F = Eq

F = kQqr2

Units N

Type vector

Direction likes repel unlikes attract

Sign donrsquot use when calculating ndash check frame of reference

One object needed ndash property of the field

Magnitude V = EPq

V = kQr

Units JC

Type scalar (+-)

Sign use sign of Q

Two objects needed ndash quantity possessed by the system

Magnitude EP = qV

EP = kQqr

Units J

Type scalar (+-)

Sign use signs of Q and q

One object needed ndash property of that one object

Magnitude E = Fq

E = kQr2

Units NC

Type vector

Direction away from positive towards negative

Sign donrsquot use when calculating ndash check frame of reference

F = 0 where E = 0 EP = 0 where V = 0

IB 12

11

DO 1 a) Calculate the net electric field at each spot (A and B)

b) Calculate the net electric force on a proton placed at each spot

DO 2 a) Calculate the net electric potential at each spot (A and B)

b) Calculate the electric potential energy of a proton placed at each spot

IB 12

12

Electric Potential and Conductors

For a hollow or solid conductor

1 all the charge resides on the outside surface

2 the electric field is zero everywhere within

3 the external electric field acts as if all the charge is concentrated at the center

4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance

Elec

tric

Fiel

d St

reng

th

Value at surface = kQr2

radius

Graphs for a spherical conductor

Distance

Elec

tric

Pote

ntia

l

radius

DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC

a) What is the electric field at the center of the sphere

b) What is the electric field at the surface of the sphere

c) What is the electric field at a distance of 075 m from the surface of the sphere

d) What is the electric potential at the surface of the sphere

e) What is the electric potential at the center of the sphere

f) What is the electric potential at a distance of 075 m from the surface of the sphere

IB 12

13

Equipotential Surfaces

Equipotential surface a surface on which the electric potential is the same everywhere

1 Locate points that are at the same electric potential around each of the point charges shown

2 Sketch in the electric field lines for each point charge

3 What is the relationship between the electric field lines and the equipotential surfaces

PerpendicularField lines point in direction

of decreasing potential

Electric Potential Gradient

The electric field strength is the negative of the electric potential gradient

Formula

Units Nc or Vm

For each electric field shown sketch in equipotential surfaces

Sketch in equipotential surfaces for the two configurations of point charges below

httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html

IB 12

3

The Principle of Superposition

The net electric force acting on a charged particle is the vector sum of all the electric forces acting on it

DO 1 Determine the net electrostatic force on charge q1 as shown below

DO 2 Where can a third charge of +10 microC be placed so that the net force acting on it is zero

DO 3 Three point charges of -20 microC are arranged as shown Determine the magnitude and direction of the net force on charge q1

IB 12

4

Electric Field

Electric field a region in space surrounding a charged object in which a second charged object experiences an electric force

Test charge a small positive charge used to test an electric field

Electric Field Diagrams (DO ALL 7)1 Positively charged sphere 2 Positive point charge 3 Negative point charge

Radial Field field lines are extensions of radii

4 Two positive charges 5 Two negative charges 6 Two unlike charges

Properties of Electric Field Lines

1 Never cross

2 Show the direction of force on a small positive test charge

3 Out of positive into negative

4 Direction of electric field is tangent to the field lines

5 Density of field lines is proportional to field strength (density = intensity)

6 Perpendicular to surface

7 Most intense near sharp points

7 Oppositely charged parallel plates

Edge Effect bowing of field lines at edges

Uniform Field field has same intensity at all spots

IB 12

5

Electric Field Strength (Intensity) electric force exerted per unit charge on a small positive test charge

Electric Field Strength

Units NC

Electric Field Electric Field for a Point Charge

Point Charge Spherical Conductor

DO 1 a) Find the magnitude and direction of the electric field at a spot 0028 meter away from a sphere whose charge is +354 microcoulombs and whose radius is 060 centimeters

b) Find the magnitude and direction of the electric force acting on a -702 nC charge placed at this spot

c) Find the electric field strength at the surface of the sphere

DO 2 a) Find the magnitude and direction of the gravitational field at an altitude of 100 km above the surface of the Earth

b) Find the magnitude and direction of the gravitational force exerted on a 60 kg bowling ball placed at this spot

c) Find the gravitational field strength at the surface of the Earth

Electric Force

Units N

IB 12

6

DO 3 a) Find the magnitude and direction of the net electric field halfway between the two charges shown below

b) Determine the electric force on a proton placed at this spot

DO 4 Two charged objects A and B each contribute as follows to the net electric field at point P EA = 300 NC directed to the right

and EB = 200 NC directed downward What is the net electric field at P

DO 5 a) Two positive point charges q1 = +16 C and q2 = +40 C are separated in a vacuum by a distance of 30 m Find the

spot on the line between the charges where the net electric field is zero

IB 12

7

DO 6 A proton is released from rest near the positive plate The distance between the plates is 30 mm and the strength of the electric field is 40 x 103 NC

a) Describe the motion of the proton

b) Write an expression for the acceleration of the proton

c) Find the time it takes the proton to reach the negative plate d) Find the speed of the proton when it reaches the negative plate

DO 7 A particle is shot with an initial speed through the two parallel plates as shown

a) Sketch and describe the path it will take if it is a proton an electron or a neutron

b) Which particle will experience a greater force

c) Which particle will experience a greater acceleration

d) Which particle will experience a greater displacement

DO 8 In the figure an electron enters the lower left side of a parallel plate capacitor and exits at the upper right side The initial speed of the electron is 550times106 ms The plates are 350 cm long and are separated by 0450 cm Assume that the electric field between the plates is uniform everywhere and find its magnitude

IB 12

8

Electric Potential Energy

Gravitational Potential Energy (EP)

Base level where EP = 0

High amount of EP

Low amount of EP

Reason for EP

1 Test object has mass (test mass = m)

2 Test mass is in a gravitational field (g) caused by larger object (M)

3 Larger object exerts a gravitational force on test mass (Fg = mg)

4 Test mass has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Gravitational potential energyEP = mgh W = ΔEP = mg Δh

Electric Potential Energy (EP)

High amount of EP

Low amount of EP

Reason for EP

1 Test object has charge (test charge = +q)

2 Test charge is in an electric field caused by larger object (Q)

3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Electric potential energyEP = Eq hW = ΔEP = Eq Δh

Base level where EP = 0

Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field

EP = 0(Work done by field)

Derivation for Point Charges

Electric Potential Energy due to a point charge

Formula Units

J

Type

scalar

IB 12

9

Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field

Electric Potential due to a point charge

Formula

Units

JC= volts(V)

Type

scalar

ABHigher potential Lower potential

Zero potential

AB

Lower potential Higher potentialZero potential

DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge

b) How much potential energy will an electron have if it is at this spot

c What is the potential where a proton is placed 096 m from a -12 nC charge

IB 12

10

Point Charges

+Q +Q +Q +Q

Electric Force Electric Field Electric Potential Energy Electric Potential

Two objects needed ndash interaction between the two

Magnitude F = Eq

F = kQqr2

Units N

Type vector

Direction likes repel unlikes attract

Sign donrsquot use when calculating ndash check frame of reference

One object needed ndash property of the field

Magnitude V = EPq

V = kQr

Units JC

Type scalar (+-)

Sign use sign of Q

Two objects needed ndash quantity possessed by the system

Magnitude EP = qV

EP = kQqr

Units J

Type scalar (+-)

Sign use signs of Q and q

One object needed ndash property of that one object

Magnitude E = Fq

E = kQr2

Units NC

Type vector

Direction away from positive towards negative

Sign donrsquot use when calculating ndash check frame of reference

F = 0 where E = 0 EP = 0 where V = 0

IB 12

11

DO 1 a) Calculate the net electric field at each spot (A and B)

b) Calculate the net electric force on a proton placed at each spot

DO 2 a) Calculate the net electric potential at each spot (A and B)

b) Calculate the electric potential energy of a proton placed at each spot

IB 12

12

Electric Potential and Conductors

For a hollow or solid conductor

1 all the charge resides on the outside surface

2 the electric field is zero everywhere within

3 the external electric field acts as if all the charge is concentrated at the center

4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance

Elec

tric

Fiel

d St

reng

th

Value at surface = kQr2

radius

Graphs for a spherical conductor

Distance

Elec

tric

Pote

ntia

l

radius

DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC

a) What is the electric field at the center of the sphere

b) What is the electric field at the surface of the sphere

c) What is the electric field at a distance of 075 m from the surface of the sphere

d) What is the electric potential at the surface of the sphere

e) What is the electric potential at the center of the sphere

f) What is the electric potential at a distance of 075 m from the surface of the sphere

IB 12

13

Equipotential Surfaces

Equipotential surface a surface on which the electric potential is the same everywhere

1 Locate points that are at the same electric potential around each of the point charges shown

2 Sketch in the electric field lines for each point charge

3 What is the relationship between the electric field lines and the equipotential surfaces

PerpendicularField lines point in direction

of decreasing potential

Electric Potential Gradient

The electric field strength is the negative of the electric potential gradient

Formula

Units Nc or Vm

For each electric field shown sketch in equipotential surfaces

Sketch in equipotential surfaces for the two configurations of point charges below

httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html

IB 12

4

Electric Field

Electric field a region in space surrounding a charged object in which a second charged object experiences an electric force

Test charge a small positive charge used to test an electric field

Electric Field Diagrams (DO ALL 7)1 Positively charged sphere 2 Positive point charge 3 Negative point charge

Radial Field field lines are extensions of radii

4 Two positive charges 5 Two negative charges 6 Two unlike charges

Properties of Electric Field Lines

1 Never cross

2 Show the direction of force on a small positive test charge

3 Out of positive into negative

4 Direction of electric field is tangent to the field lines

5 Density of field lines is proportional to field strength (density = intensity)

6 Perpendicular to surface

7 Most intense near sharp points

7 Oppositely charged parallel plates

Edge Effect bowing of field lines at edges

Uniform Field field has same intensity at all spots

IB 12

5

Electric Field Strength (Intensity) electric force exerted per unit charge on a small positive test charge

Electric Field Strength

Units NC

Electric Field Electric Field for a Point Charge

Point Charge Spherical Conductor

DO 1 a) Find the magnitude and direction of the electric field at a spot 0028 meter away from a sphere whose charge is +354 microcoulombs and whose radius is 060 centimeters

b) Find the magnitude and direction of the electric force acting on a -702 nC charge placed at this spot

c) Find the electric field strength at the surface of the sphere

DO 2 a) Find the magnitude and direction of the gravitational field at an altitude of 100 km above the surface of the Earth

b) Find the magnitude and direction of the gravitational force exerted on a 60 kg bowling ball placed at this spot

c) Find the gravitational field strength at the surface of the Earth

Electric Force

Units N

IB 12

6

DO 3 a) Find the magnitude and direction of the net electric field halfway between the two charges shown below

b) Determine the electric force on a proton placed at this spot

DO 4 Two charged objects A and B each contribute as follows to the net electric field at point P EA = 300 NC directed to the right

and EB = 200 NC directed downward What is the net electric field at P

DO 5 a) Two positive point charges q1 = +16 C and q2 = +40 C are separated in a vacuum by a distance of 30 m Find the

spot on the line between the charges where the net electric field is zero

IB 12

7

DO 6 A proton is released from rest near the positive plate The distance between the plates is 30 mm and the strength of the electric field is 40 x 103 NC

a) Describe the motion of the proton

b) Write an expression for the acceleration of the proton

c) Find the time it takes the proton to reach the negative plate d) Find the speed of the proton when it reaches the negative plate

DO 7 A particle is shot with an initial speed through the two parallel plates as shown

a) Sketch and describe the path it will take if it is a proton an electron or a neutron

b) Which particle will experience a greater force

c) Which particle will experience a greater acceleration

d) Which particle will experience a greater displacement

DO 8 In the figure an electron enters the lower left side of a parallel plate capacitor and exits at the upper right side The initial speed of the electron is 550times106 ms The plates are 350 cm long and are separated by 0450 cm Assume that the electric field between the plates is uniform everywhere and find its magnitude

IB 12

8

Electric Potential Energy

Gravitational Potential Energy (EP)

Base level where EP = 0

High amount of EP

Low amount of EP

Reason for EP

1 Test object has mass (test mass = m)

2 Test mass is in a gravitational field (g) caused by larger object (M)

3 Larger object exerts a gravitational force on test mass (Fg = mg)

4 Test mass has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Gravitational potential energyEP = mgh W = ΔEP = mg Δh

Electric Potential Energy (EP)

High amount of EP

Low amount of EP

Reason for EP

1 Test object has charge (test charge = +q)

2 Test charge is in an electric field caused by larger object (Q)

3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Electric potential energyEP = Eq hW = ΔEP = Eq Δh

Base level where EP = 0

Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field

EP = 0(Work done by field)

Derivation for Point Charges

Electric Potential Energy due to a point charge

Formula Units

J

Type

scalar

IB 12

9

Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field

Electric Potential due to a point charge

Formula

Units

JC= volts(V)

Type

scalar

ABHigher potential Lower potential

Zero potential

AB

Lower potential Higher potentialZero potential

DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge

b) How much potential energy will an electron have if it is at this spot

c What is the potential where a proton is placed 096 m from a -12 nC charge

IB 12

10

Point Charges

+Q +Q +Q +Q

Electric Force Electric Field Electric Potential Energy Electric Potential

Two objects needed ndash interaction between the two

Magnitude F = Eq

F = kQqr2

Units N

Type vector

Direction likes repel unlikes attract

Sign donrsquot use when calculating ndash check frame of reference

One object needed ndash property of the field

Magnitude V = EPq

V = kQr

Units JC

Type scalar (+-)

Sign use sign of Q

Two objects needed ndash quantity possessed by the system

Magnitude EP = qV

EP = kQqr

Units J

Type scalar (+-)

Sign use signs of Q and q

One object needed ndash property of that one object

Magnitude E = Fq

E = kQr2

Units NC

Type vector

Direction away from positive towards negative

Sign donrsquot use when calculating ndash check frame of reference

F = 0 where E = 0 EP = 0 where V = 0

IB 12

11

DO 1 a) Calculate the net electric field at each spot (A and B)

b) Calculate the net electric force on a proton placed at each spot

DO 2 a) Calculate the net electric potential at each spot (A and B)

b) Calculate the electric potential energy of a proton placed at each spot

IB 12

12

Electric Potential and Conductors

For a hollow or solid conductor

1 all the charge resides on the outside surface

2 the electric field is zero everywhere within

3 the external electric field acts as if all the charge is concentrated at the center

4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance

Elec

tric

Fiel

d St

reng

th

Value at surface = kQr2

radius

Graphs for a spherical conductor

Distance

Elec

tric

Pote

ntia

l

radius

DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC

a) What is the electric field at the center of the sphere

b) What is the electric field at the surface of the sphere

c) What is the electric field at a distance of 075 m from the surface of the sphere

d) What is the electric potential at the surface of the sphere

e) What is the electric potential at the center of the sphere

f) What is the electric potential at a distance of 075 m from the surface of the sphere

IB 12

13

Equipotential Surfaces

Equipotential surface a surface on which the electric potential is the same everywhere

1 Locate points that are at the same electric potential around each of the point charges shown

2 Sketch in the electric field lines for each point charge

3 What is the relationship between the electric field lines and the equipotential surfaces

PerpendicularField lines point in direction

of decreasing potential

Electric Potential Gradient

The electric field strength is the negative of the electric potential gradient

Formula

Units Nc or Vm

For each electric field shown sketch in equipotential surfaces

Sketch in equipotential surfaces for the two configurations of point charges below

httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html

IB 12

5

Electric Field Strength (Intensity) electric force exerted per unit charge on a small positive test charge

Electric Field Strength

Units NC

Electric Field Electric Field for a Point Charge

Point Charge Spherical Conductor

DO 1 a) Find the magnitude and direction of the electric field at a spot 0028 meter away from a sphere whose charge is +354 microcoulombs and whose radius is 060 centimeters

b) Find the magnitude and direction of the electric force acting on a -702 nC charge placed at this spot

c) Find the electric field strength at the surface of the sphere

DO 2 a) Find the magnitude and direction of the gravitational field at an altitude of 100 km above the surface of the Earth

b) Find the magnitude and direction of the gravitational force exerted on a 60 kg bowling ball placed at this spot

c) Find the gravitational field strength at the surface of the Earth

Electric Force

Units N

IB 12

6

DO 3 a) Find the magnitude and direction of the net electric field halfway between the two charges shown below

b) Determine the electric force on a proton placed at this spot

DO 4 Two charged objects A and B each contribute as follows to the net electric field at point P EA = 300 NC directed to the right

and EB = 200 NC directed downward What is the net electric field at P

DO 5 a) Two positive point charges q1 = +16 C and q2 = +40 C are separated in a vacuum by a distance of 30 m Find the

spot on the line between the charges where the net electric field is zero

IB 12

7

DO 6 A proton is released from rest near the positive plate The distance between the plates is 30 mm and the strength of the electric field is 40 x 103 NC

a) Describe the motion of the proton

b) Write an expression for the acceleration of the proton

c) Find the time it takes the proton to reach the negative plate d) Find the speed of the proton when it reaches the negative plate

DO 7 A particle is shot with an initial speed through the two parallel plates as shown

a) Sketch and describe the path it will take if it is a proton an electron or a neutron

b) Which particle will experience a greater force

c) Which particle will experience a greater acceleration

d) Which particle will experience a greater displacement

DO 8 In the figure an electron enters the lower left side of a parallel plate capacitor and exits at the upper right side The initial speed of the electron is 550times106 ms The plates are 350 cm long and are separated by 0450 cm Assume that the electric field between the plates is uniform everywhere and find its magnitude

IB 12

8

Electric Potential Energy

Gravitational Potential Energy (EP)

Base level where EP = 0

High amount of EP

Low amount of EP

Reason for EP

1 Test object has mass (test mass = m)

2 Test mass is in a gravitational field (g) caused by larger object (M)

3 Larger object exerts a gravitational force on test mass (Fg = mg)

4 Test mass has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Gravitational potential energyEP = mgh W = ΔEP = mg Δh

Electric Potential Energy (EP)

High amount of EP

Low amount of EP

Reason for EP

1 Test object has charge (test charge = +q)

2 Test charge is in an electric field caused by larger object (Q)

3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Electric potential energyEP = Eq hW = ΔEP = Eq Δh

Base level where EP = 0

Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field

EP = 0(Work done by field)

Derivation for Point Charges

Electric Potential Energy due to a point charge

Formula Units

J

Type

scalar

IB 12

9

Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field

Electric Potential due to a point charge

Formula

Units

JC= volts(V)

Type

scalar

ABHigher potential Lower potential

Zero potential

AB

Lower potential Higher potentialZero potential

DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge

b) How much potential energy will an electron have if it is at this spot

c What is the potential where a proton is placed 096 m from a -12 nC charge

IB 12

10

Point Charges

+Q +Q +Q +Q

Electric Force Electric Field Electric Potential Energy Electric Potential

Two objects needed ndash interaction between the two

Magnitude F = Eq

F = kQqr2

Units N

Type vector

Direction likes repel unlikes attract

Sign donrsquot use when calculating ndash check frame of reference

One object needed ndash property of the field

Magnitude V = EPq

V = kQr

Units JC

Type scalar (+-)

Sign use sign of Q

Two objects needed ndash quantity possessed by the system

Magnitude EP = qV

EP = kQqr

Units J

Type scalar (+-)

Sign use signs of Q and q

One object needed ndash property of that one object

Magnitude E = Fq

E = kQr2

Units NC

Type vector

Direction away from positive towards negative

Sign donrsquot use when calculating ndash check frame of reference

F = 0 where E = 0 EP = 0 where V = 0

IB 12

11

DO 1 a) Calculate the net electric field at each spot (A and B)

b) Calculate the net electric force on a proton placed at each spot

DO 2 a) Calculate the net electric potential at each spot (A and B)

b) Calculate the electric potential energy of a proton placed at each spot

IB 12

12

Electric Potential and Conductors

For a hollow or solid conductor

1 all the charge resides on the outside surface

2 the electric field is zero everywhere within

3 the external electric field acts as if all the charge is concentrated at the center

4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance

Elec

tric

Fiel

d St

reng

th

Value at surface = kQr2

radius

Graphs for a spherical conductor

Distance

Elec

tric

Pote

ntia

l

radius

DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC

a) What is the electric field at the center of the sphere

b) What is the electric field at the surface of the sphere

c) What is the electric field at a distance of 075 m from the surface of the sphere

d) What is the electric potential at the surface of the sphere

e) What is the electric potential at the center of the sphere

f) What is the electric potential at a distance of 075 m from the surface of the sphere

IB 12

13

Equipotential Surfaces

Equipotential surface a surface on which the electric potential is the same everywhere

1 Locate points that are at the same electric potential around each of the point charges shown

2 Sketch in the electric field lines for each point charge

3 What is the relationship between the electric field lines and the equipotential surfaces

PerpendicularField lines point in direction

of decreasing potential

Electric Potential Gradient

The electric field strength is the negative of the electric potential gradient

Formula

Units Nc or Vm

For each electric field shown sketch in equipotential surfaces

Sketch in equipotential surfaces for the two configurations of point charges below

httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html

IB 12

6

DO 3 a) Find the magnitude and direction of the net electric field halfway between the two charges shown below

b) Determine the electric force on a proton placed at this spot

DO 4 Two charged objects A and B each contribute as follows to the net electric field at point P EA = 300 NC directed to the right

and EB = 200 NC directed downward What is the net electric field at P

DO 5 a) Two positive point charges q1 = +16 C and q2 = +40 C are separated in a vacuum by a distance of 30 m Find the

spot on the line between the charges where the net electric field is zero

IB 12

7

DO 6 A proton is released from rest near the positive plate The distance between the plates is 30 mm and the strength of the electric field is 40 x 103 NC

a) Describe the motion of the proton

b) Write an expression for the acceleration of the proton

c) Find the time it takes the proton to reach the negative plate d) Find the speed of the proton when it reaches the negative plate

DO 7 A particle is shot with an initial speed through the two parallel plates as shown

a) Sketch and describe the path it will take if it is a proton an electron or a neutron

b) Which particle will experience a greater force

c) Which particle will experience a greater acceleration

d) Which particle will experience a greater displacement

DO 8 In the figure an electron enters the lower left side of a parallel plate capacitor and exits at the upper right side The initial speed of the electron is 550times106 ms The plates are 350 cm long and are separated by 0450 cm Assume that the electric field between the plates is uniform everywhere and find its magnitude

IB 12

8

Electric Potential Energy

Gravitational Potential Energy (EP)

Base level where EP = 0

High amount of EP

Low amount of EP

Reason for EP

1 Test object has mass (test mass = m)

2 Test mass is in a gravitational field (g) caused by larger object (M)

3 Larger object exerts a gravitational force on test mass (Fg = mg)

4 Test mass has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Gravitational potential energyEP = mgh W = ΔEP = mg Δh

Electric Potential Energy (EP)

High amount of EP

Low amount of EP

Reason for EP

1 Test object has charge (test charge = +q)

2 Test charge is in an electric field caused by larger object (Q)

3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Electric potential energyEP = Eq hW = ΔEP = Eq Δh

Base level where EP = 0

Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field

EP = 0(Work done by field)

Derivation for Point Charges

Electric Potential Energy due to a point charge

Formula Units

J

Type

scalar

IB 12

9

Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field

Electric Potential due to a point charge

Formula

Units

JC= volts(V)

Type

scalar

ABHigher potential Lower potential

Zero potential

AB

Lower potential Higher potentialZero potential

DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge

b) How much potential energy will an electron have if it is at this spot

c What is the potential where a proton is placed 096 m from a -12 nC charge

IB 12

10

Point Charges

+Q +Q +Q +Q

Electric Force Electric Field Electric Potential Energy Electric Potential

Two objects needed ndash interaction between the two

Magnitude F = Eq

F = kQqr2

Units N

Type vector

Direction likes repel unlikes attract

Sign donrsquot use when calculating ndash check frame of reference

One object needed ndash property of the field

Magnitude V = EPq

V = kQr

Units JC

Type scalar (+-)

Sign use sign of Q

Two objects needed ndash quantity possessed by the system

Magnitude EP = qV

EP = kQqr

Units J

Type scalar (+-)

Sign use signs of Q and q

One object needed ndash property of that one object

Magnitude E = Fq

E = kQr2

Units NC

Type vector

Direction away from positive towards negative

Sign donrsquot use when calculating ndash check frame of reference

F = 0 where E = 0 EP = 0 where V = 0

IB 12

11

DO 1 a) Calculate the net electric field at each spot (A and B)

b) Calculate the net electric force on a proton placed at each spot

DO 2 a) Calculate the net electric potential at each spot (A and B)

b) Calculate the electric potential energy of a proton placed at each spot

IB 12

12

Electric Potential and Conductors

For a hollow or solid conductor

1 all the charge resides on the outside surface

2 the electric field is zero everywhere within

3 the external electric field acts as if all the charge is concentrated at the center

4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance

Elec

tric

Fiel

d St

reng

th

Value at surface = kQr2

radius

Graphs for a spherical conductor

Distance

Elec

tric

Pote

ntia

l

radius

DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC

a) What is the electric field at the center of the sphere

b) What is the electric field at the surface of the sphere

c) What is the electric field at a distance of 075 m from the surface of the sphere

d) What is the electric potential at the surface of the sphere

e) What is the electric potential at the center of the sphere

f) What is the electric potential at a distance of 075 m from the surface of the sphere

IB 12

13

Equipotential Surfaces

Equipotential surface a surface on which the electric potential is the same everywhere

1 Locate points that are at the same electric potential around each of the point charges shown

2 Sketch in the electric field lines for each point charge

3 What is the relationship between the electric field lines and the equipotential surfaces

PerpendicularField lines point in direction

of decreasing potential

Electric Potential Gradient

The electric field strength is the negative of the electric potential gradient

Formula

Units Nc or Vm

For each electric field shown sketch in equipotential surfaces

Sketch in equipotential surfaces for the two configurations of point charges below

httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html

IB 12

7

DO 6 A proton is released from rest near the positive plate The distance between the plates is 30 mm and the strength of the electric field is 40 x 103 NC

a) Describe the motion of the proton

b) Write an expression for the acceleration of the proton

c) Find the time it takes the proton to reach the negative plate d) Find the speed of the proton when it reaches the negative plate

DO 7 A particle is shot with an initial speed through the two parallel plates as shown

a) Sketch and describe the path it will take if it is a proton an electron or a neutron

b) Which particle will experience a greater force

c) Which particle will experience a greater acceleration

d) Which particle will experience a greater displacement

DO 8 In the figure an electron enters the lower left side of a parallel plate capacitor and exits at the upper right side The initial speed of the electron is 550times106 ms The plates are 350 cm long and are separated by 0450 cm Assume that the electric field between the plates is uniform everywhere and find its magnitude

IB 12

8

Electric Potential Energy

Gravitational Potential Energy (EP)

Base level where EP = 0

High amount of EP

Low amount of EP

Reason for EP

1 Test object has mass (test mass = m)

2 Test mass is in a gravitational field (g) caused by larger object (M)

3 Larger object exerts a gravitational force on test mass (Fg = mg)

4 Test mass has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Gravitational potential energyEP = mgh W = ΔEP = mg Δh

Electric Potential Energy (EP)

High amount of EP

Low amount of EP

Reason for EP

1 Test object has charge (test charge = +q)

2 Test charge is in an electric field caused by larger object (Q)

3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Electric potential energyEP = Eq hW = ΔEP = Eq Δh

Base level where EP = 0

Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field

EP = 0(Work done by field)

Derivation for Point Charges

Electric Potential Energy due to a point charge

Formula Units

J

Type

scalar

IB 12

9

Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field

Electric Potential due to a point charge

Formula

Units

JC= volts(V)

Type

scalar

ABHigher potential Lower potential

Zero potential

AB

Lower potential Higher potentialZero potential

DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge

b) How much potential energy will an electron have if it is at this spot

c What is the potential where a proton is placed 096 m from a -12 nC charge

IB 12

10

Point Charges

+Q +Q +Q +Q

Electric Force Electric Field Electric Potential Energy Electric Potential

Two objects needed ndash interaction between the two

Magnitude F = Eq

F = kQqr2

Units N

Type vector

Direction likes repel unlikes attract

Sign donrsquot use when calculating ndash check frame of reference

One object needed ndash property of the field

Magnitude V = EPq

V = kQr

Units JC

Type scalar (+-)

Sign use sign of Q

Two objects needed ndash quantity possessed by the system

Magnitude EP = qV

EP = kQqr

Units J

Type scalar (+-)

Sign use signs of Q and q

One object needed ndash property of that one object

Magnitude E = Fq

E = kQr2

Units NC

Type vector

Direction away from positive towards negative

Sign donrsquot use when calculating ndash check frame of reference

F = 0 where E = 0 EP = 0 where V = 0

IB 12

11

DO 1 a) Calculate the net electric field at each spot (A and B)

b) Calculate the net electric force on a proton placed at each spot

DO 2 a) Calculate the net electric potential at each spot (A and B)

b) Calculate the electric potential energy of a proton placed at each spot

IB 12

12

Electric Potential and Conductors

For a hollow or solid conductor

1 all the charge resides on the outside surface

2 the electric field is zero everywhere within

3 the external electric field acts as if all the charge is concentrated at the center

4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance

Elec

tric

Fiel

d St

reng

th

Value at surface = kQr2

radius

Graphs for a spherical conductor

Distance

Elec

tric

Pote

ntia

l

radius

DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC

a) What is the electric field at the center of the sphere

b) What is the electric field at the surface of the sphere

c) What is the electric field at a distance of 075 m from the surface of the sphere

d) What is the electric potential at the surface of the sphere

e) What is the electric potential at the center of the sphere

f) What is the electric potential at a distance of 075 m from the surface of the sphere

IB 12

13

Equipotential Surfaces

Equipotential surface a surface on which the electric potential is the same everywhere

1 Locate points that are at the same electric potential around each of the point charges shown

2 Sketch in the electric field lines for each point charge

3 What is the relationship between the electric field lines and the equipotential surfaces

PerpendicularField lines point in direction

of decreasing potential

Electric Potential Gradient

The electric field strength is the negative of the electric potential gradient

Formula

Units Nc or Vm

For each electric field shown sketch in equipotential surfaces

Sketch in equipotential surfaces for the two configurations of point charges below

httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html

IB 12

8

Electric Potential Energy

Gravitational Potential Energy (EP)

Base level where EP = 0

High amount of EP

Low amount of EP

Reason for EP

1 Test object has mass (test mass = m)

2 Test mass is in a gravitational field (g) caused by larger object (M)

3 Larger object exerts a gravitational force on test mass (Fg = mg)

4 Test mass has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Gravitational potential energyEP = mgh W = ΔEP = mg Δh

Electric Potential Energy (EP)

High amount of EP

Low amount of EP

Reason for EP

1 Test object has charge (test charge = +q)

2 Test charge is in an electric field caused by larger object (Q)

3 Larger object exerts an electric force on test charge (FE = Eq) 4 Test charge has tendency to move to base level due to force

5 Work done moving object between two positions is path independent

Electric potential energyEP = Eq hW = ΔEP = Eq Δh

Base level where EP = 0

Electric Potential Energy (EP)- the work done in bringing a small positive test charge in from infinity to that point in the electric field

EP = 0(Work done by field)

Derivation for Point Charges

Electric Potential Energy due to a point charge

Formula Units

J

Type

scalar

IB 12

9

Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field

Electric Potential due to a point charge

Formula

Units

JC= volts(V)

Type

scalar

ABHigher potential Lower potential

Zero potential

AB

Lower potential Higher potentialZero potential

DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge

b) How much potential energy will an electron have if it is at this spot

c What is the potential where a proton is placed 096 m from a -12 nC charge

IB 12

10

Point Charges

+Q +Q +Q +Q

Electric Force Electric Field Electric Potential Energy Electric Potential

Two objects needed ndash interaction between the two

Magnitude F = Eq

F = kQqr2

Units N

Type vector

Direction likes repel unlikes attract

Sign donrsquot use when calculating ndash check frame of reference

One object needed ndash property of the field

Magnitude V = EPq

V = kQr

Units JC

Type scalar (+-)

Sign use sign of Q

Two objects needed ndash quantity possessed by the system

Magnitude EP = qV

EP = kQqr

Units J

Type scalar (+-)

Sign use signs of Q and q

One object needed ndash property of that one object

Magnitude E = Fq

E = kQr2

Units NC

Type vector

Direction away from positive towards negative

Sign donrsquot use when calculating ndash check frame of reference

F = 0 where E = 0 EP = 0 where V = 0

IB 12

11

DO 1 a) Calculate the net electric field at each spot (A and B)

b) Calculate the net electric force on a proton placed at each spot

DO 2 a) Calculate the net electric potential at each spot (A and B)

b) Calculate the electric potential energy of a proton placed at each spot

IB 12

12

Electric Potential and Conductors

For a hollow or solid conductor

1 all the charge resides on the outside surface

2 the electric field is zero everywhere within

3 the external electric field acts as if all the charge is concentrated at the center

4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance

Elec

tric

Fiel

d St

reng

th

Value at surface = kQr2

radius

Graphs for a spherical conductor

Distance

Elec

tric

Pote

ntia

l

radius

DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC

a) What is the electric field at the center of the sphere

b) What is the electric field at the surface of the sphere

c) What is the electric field at a distance of 075 m from the surface of the sphere

d) What is the electric potential at the surface of the sphere

e) What is the electric potential at the center of the sphere

f) What is the electric potential at a distance of 075 m from the surface of the sphere

IB 12

13

Equipotential Surfaces

Equipotential surface a surface on which the electric potential is the same everywhere

1 Locate points that are at the same electric potential around each of the point charges shown

2 Sketch in the electric field lines for each point charge

3 What is the relationship between the electric field lines and the equipotential surfaces

PerpendicularField lines point in direction

of decreasing potential

Electric Potential Gradient

The electric field strength is the negative of the electric potential gradient

Formula

Units Nc or Vm

For each electric field shown sketch in equipotential surfaces

Sketch in equipotential surfaces for the two configurations of point charges below

httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html

IB 12

9

Electric Potential (V) - work done per unit charge moving a small positive test charge in from infinity to a point in an electric field

Electric Potential due to a point charge

Formula

Units

JC= volts(V)

Type

scalar

ABHigher potential Lower potential

Zero potential

AB

Lower potential Higher potentialZero potential

DO 1 a) Calculate the potential at a point 250 cm away from a +48 μC charge

b) How much potential energy will an electron have if it is at this spot

c What is the potential where a proton is placed 096 m from a -12 nC charge

IB 12

10

Point Charges

+Q +Q +Q +Q

Electric Force Electric Field Electric Potential Energy Electric Potential

Two objects needed ndash interaction between the two

Magnitude F = Eq

F = kQqr2

Units N

Type vector

Direction likes repel unlikes attract

Sign donrsquot use when calculating ndash check frame of reference

One object needed ndash property of the field

Magnitude V = EPq

V = kQr

Units JC

Type scalar (+-)

Sign use sign of Q

Two objects needed ndash quantity possessed by the system

Magnitude EP = qV

EP = kQqr

Units J

Type scalar (+-)

Sign use signs of Q and q

One object needed ndash property of that one object

Magnitude E = Fq

E = kQr2

Units NC

Type vector

Direction away from positive towards negative

Sign donrsquot use when calculating ndash check frame of reference

F = 0 where E = 0 EP = 0 where V = 0

IB 12

11

DO 1 a) Calculate the net electric field at each spot (A and B)

b) Calculate the net electric force on a proton placed at each spot

DO 2 a) Calculate the net electric potential at each spot (A and B)

b) Calculate the electric potential energy of a proton placed at each spot

IB 12

12

Electric Potential and Conductors

For a hollow or solid conductor

1 all the charge resides on the outside surface

2 the electric field is zero everywhere within

3 the external electric field acts as if all the charge is concentrated at the center

4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance

Elec

tric

Fiel

d St

reng

th

Value at surface = kQr2

radius

Graphs for a spherical conductor

Distance

Elec

tric

Pote

ntia

l

radius

DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC

a) What is the electric field at the center of the sphere

b) What is the electric field at the surface of the sphere

c) What is the electric field at a distance of 075 m from the surface of the sphere

d) What is the electric potential at the surface of the sphere

e) What is the electric potential at the center of the sphere

f) What is the electric potential at a distance of 075 m from the surface of the sphere

IB 12

13

Equipotential Surfaces

Equipotential surface a surface on which the electric potential is the same everywhere

1 Locate points that are at the same electric potential around each of the point charges shown

2 Sketch in the electric field lines for each point charge

3 What is the relationship between the electric field lines and the equipotential surfaces

PerpendicularField lines point in direction

of decreasing potential

Electric Potential Gradient

The electric field strength is the negative of the electric potential gradient

Formula

Units Nc or Vm

For each electric field shown sketch in equipotential surfaces

Sketch in equipotential surfaces for the two configurations of point charges below

httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html

IB 12

10

Point Charges

+Q +Q +Q +Q

Electric Force Electric Field Electric Potential Energy Electric Potential

Two objects needed ndash interaction between the two

Magnitude F = Eq

F = kQqr2

Units N

Type vector

Direction likes repel unlikes attract

Sign donrsquot use when calculating ndash check frame of reference

One object needed ndash property of the field

Magnitude V = EPq

V = kQr

Units JC

Type scalar (+-)

Sign use sign of Q

Two objects needed ndash quantity possessed by the system

Magnitude EP = qV

EP = kQqr

Units J

Type scalar (+-)

Sign use signs of Q and q

One object needed ndash property of that one object

Magnitude E = Fq

E = kQr2

Units NC

Type vector

Direction away from positive towards negative

Sign donrsquot use when calculating ndash check frame of reference

F = 0 where E = 0 EP = 0 where V = 0

IB 12

11

DO 1 a) Calculate the net electric field at each spot (A and B)

b) Calculate the net electric force on a proton placed at each spot

DO 2 a) Calculate the net electric potential at each spot (A and B)

b) Calculate the electric potential energy of a proton placed at each spot

IB 12

12

Electric Potential and Conductors

For a hollow or solid conductor

1 all the charge resides on the outside surface

2 the electric field is zero everywhere within

3 the external electric field acts as if all the charge is concentrated at the center

4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance

Elec

tric

Fiel

d St

reng

th

Value at surface = kQr2

radius

Graphs for a spherical conductor

Distance

Elec

tric

Pote

ntia

l

radius

DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC

a) What is the electric field at the center of the sphere

b) What is the electric field at the surface of the sphere

c) What is the electric field at a distance of 075 m from the surface of the sphere

d) What is the electric potential at the surface of the sphere

e) What is the electric potential at the center of the sphere

f) What is the electric potential at a distance of 075 m from the surface of the sphere

IB 12

13

Equipotential Surfaces

Equipotential surface a surface on which the electric potential is the same everywhere

1 Locate points that are at the same electric potential around each of the point charges shown

2 Sketch in the electric field lines for each point charge

3 What is the relationship between the electric field lines and the equipotential surfaces

PerpendicularField lines point in direction

of decreasing potential

Electric Potential Gradient

The electric field strength is the negative of the electric potential gradient

Formula

Units Nc or Vm

For each electric field shown sketch in equipotential surfaces

Sketch in equipotential surfaces for the two configurations of point charges below

httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html

IB 12

11

DO 1 a) Calculate the net electric field at each spot (A and B)

b) Calculate the net electric force on a proton placed at each spot

DO 2 a) Calculate the net electric potential at each spot (A and B)

b) Calculate the electric potential energy of a proton placed at each spot

IB 12

12

Electric Potential and Conductors

For a hollow or solid conductor

1 all the charge resides on the outside surface

2 the electric field is zero everywhere within

3 the external electric field acts as if all the charge is concentrated at the center

4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance

Elec

tric

Fiel

d St

reng

th

Value at surface = kQr2

radius

Graphs for a spherical conductor

Distance

Elec

tric

Pote

ntia

l

radius

DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC

a) What is the electric field at the center of the sphere

b) What is the electric field at the surface of the sphere

c) What is the electric field at a distance of 075 m from the surface of the sphere

d) What is the electric potential at the surface of the sphere

e) What is the electric potential at the center of the sphere

f) What is the electric potential at a distance of 075 m from the surface of the sphere

IB 12

13

Equipotential Surfaces

Equipotential surface a surface on which the electric potential is the same everywhere

1 Locate points that are at the same electric potential around each of the point charges shown

2 Sketch in the electric field lines for each point charge

3 What is the relationship between the electric field lines and the equipotential surfaces

PerpendicularField lines point in direction

of decreasing potential

Electric Potential Gradient

The electric field strength is the negative of the electric potential gradient

Formula

Units Nc or Vm

For each electric field shown sketch in equipotential surfaces

Sketch in equipotential surfaces for the two configurations of point charges below

httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html

IB 12

12

Electric Potential and Conductors

For a hollow or solid conductor

1 all the charge resides on the outside surface

2 the electric field is zero everywhere within

3 the external electric field acts as if all the charge is concentrated at the center

4 the electric potential is constant (ne 0) everywhere within and equal to the potential at the surface Distance

Elec

tric

Fiel

d St

reng

th

Value at surface = kQr2

radius

Graphs for a spherical conductor

Distance

Elec

tric

Pote

ntia

l

radius

DO 1 A spherical conducting surface whose radius is 075 m has a net charge of +48 μC

a) What is the electric field at the center of the sphere

b) What is the electric field at the surface of the sphere

c) What is the electric field at a distance of 075 m from the surface of the sphere

d) What is the electric potential at the surface of the sphere

e) What is the electric potential at the center of the sphere

f) What is the electric potential at a distance of 075 m from the surface of the sphere

IB 12

13

Equipotential Surfaces

Equipotential surface a surface on which the electric potential is the same everywhere

1 Locate points that are at the same electric potential around each of the point charges shown

2 Sketch in the electric field lines for each point charge

3 What is the relationship between the electric field lines and the equipotential surfaces

PerpendicularField lines point in direction

of decreasing potential

Electric Potential Gradient

The electric field strength is the negative of the electric potential gradient

Formula

Units Nc or Vm

For each electric field shown sketch in equipotential surfaces

Sketch in equipotential surfaces for the two configurations of point charges below

httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html

IB 12

13

Equipotential Surfaces

Equipotential surface a surface on which the electric potential is the same everywhere

1 Locate points that are at the same electric potential around each of the point charges shown

2 Sketch in the electric field lines for each point charge

3 What is the relationship between the electric field lines and the equipotential surfaces

PerpendicularField lines point in direction

of decreasing potential

Electric Potential Gradient

The electric field strength is the negative of the electric potential gradient

Formula

Units Nc or Vm

For each electric field shown sketch in equipotential surfaces

Sketch in equipotential surfaces for the two configurations of point charges below

httpwwwsurendranathorgAppletshtmlhttpwpsawcomaw_young_physics_1108076898593-00html

IB 12

14

Electric Potential Difference (ΔV) ndash work done per unit charge moving a small positive test charge between two points in an electric field

Electric Potential Difference

Formula

Units JC = V

High and Low Potential

DO 1 a) Which plate is at a higher electric potential

b) Which plate is at a lower electric potential

c) What is the electric potential of each plate

d) What is the potential difference between the plates Mark plates with example potentials as well as spots within fieldMark ldquogroundrdquo ndash mark equipotentials

e) Where will a proton have the most electric potential energy

an electron a neutron an alpha particle

DO 2 An electron is released from rest near the negative plate and allowed to accelerate until it hits the positive plate The distance between the plates is 200 cm and the potential difference between them is 100 volts

b) Calculate the strength of the electric field

a) Calculate how fast the electron strikes the positive plate

Formula

qV = frac12 mv2

Ve = frac12 mv2

Formula

E = -ΔVΔxE = Vd

IB 12

15

DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)

The Electronvolt

Electronvolt energy gained by an electron moving through a potential difference of one volt

ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV

ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J

Therefore 1 eV = 160 x 10-19 J

Derivation

DO 1 How much energy is gained by a proton moving through a potential difference of 150 V

DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this

DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron

IB 12

15

DO 4 In Rutherfordrsquos famous scattering experiments (which led to the planetary model of the atom) alpha particles were fired toward a gold nucleus with charge +79e An alpha particle initially very far from the gold nucleus is fired at 200 times 107 ms directly toward the gold nucleus Assume the gold nucleus remains stationary How close does the alpha particle get to the gold nucleus before turning around (the ldquodistance of closest approachrdquo)

The Electronvolt

Electronvolt energy gained by an electron moving through a potential difference of one volt

ΔEe = qΔVΔEe = (1e)(1 V) = 1 eV

ΔEe = (16 x 10-19 C)( 1 V)ΔEe = 16 x 10-19 J

Therefore 1 eV = 160 x 10-19 J

Derivation

DO 1 How much energy is gained by a proton moving through a potential difference of 150 V

DO 2 A charged particle has 54 x 10-16 J of energy How many electronvolts of energy is this

DO 3 An electron gains 200 eV accelerating from rest in a uniform electric field of 150 NC Calculate the final speed of the electron