Invention of the first Invention of the first TransistorTransistor in Nov.17in Nov.17--Dec.23 1947, Dec.23 1947, the most important invention of 20the most important invention of 20thth centurycentury

GoalsGoals

Knowledge of physics

Critical thinking, idealization, approximation, mathematical and

graphical representations of phenomena.

Physics 213

Electric Charge, Field, Energy, CurrentsMagnetismElectromagnetismLight and OpticsModern Physics including Special Relativity, Quantum Mechanics and Nuclear Physics

Chapter 15

Electric Forces Electric Fields

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Electric Charge Coulomb’s Law

Outline for Today

What is electric charge?What is electric charge?Like rest mass, it is a fundamental property of some of the elementary

particles of which all matter is composed

Electric charge is the fourth quantity

we have learned (energy, linear

momentum, and angular momentum)

Properties of Electric Charges

Two types of charges existThey are called positive and negativeNamed by Benjamin Franklin

Like charges repel and unlike charges attract one anotherNature’s basic carrier of positive charge is the proton

Protons do not move from one material to another because they are held firmly in the nucleus

More Properties of Charge

Nature’s basic carrier of negative charge is the electron

Gaining or losing electrons is how an object becomes charged

Electric charge is always conservedCharge is not created, only exchangedObjects become charged because negative charge is transferred from one object to another

Properties of Charge

Charge is quantizedAll charge is a multiple of a fundamental unit of charge, symbolized by e

Quarks are the exception

Electrons have a charge of –eProtons have a charge of +eThe SI unit of charge is the Coulomb (C)

e = 1.6 x 10-19 C

QuestionQuestion: Electric charge(a) is a continuous quantity that can be

subdivided indefinitely(b) is a continuous quantity but it cannot be

subdivided into smaller parcels than 1.6x10-

19 C(c) occurs only in separate parcels, each of

1.6x10-19 C(d) occurs only in separate parcels, each of 1 C

Answer: c

Question: A negative electric charge (a) interacts only with positive charges (b) interacts only with negative charges(c) interacts with both positive and

negative charges(d) may interact with either positive and

negative charges, depending on circumstances

Answer: c

Question: An object has a positive electric charge whenever

(a) it has an excess of electrons(b) it has a deficiency of electrons (c) the nuclei of its atoms are positively

charged (d) the electrons of its atoms are

positively charged

Answer: b

Conductors

Conductors are materials in which the electric charges move freely

Copper, aluminum and silver are good conductorsWhen a conductor is charged in a small region, the charge readily distributes itself over the entire surface of the material

0

0.1

0.2

0.3

0.4

0.5

0 200 400 600 800 1000

RuO2

T(K)

CaRuO3

SrRuO3

Mott-Ioffe-Regel limit

ρ ~T 2

ab-plane

Metal: dρ/dT>0

Insulators

Insulators are materials in which electric charges do not move freely

Glass and rubber are examples of insulatorsWhen insulators are charged by rubbing, only the rubbed area becomes charged

There is no tendency for the charge to move into other regions of the material

0.1

10

1000

105

107

109

50 100 150 200 250 300T (K)

Ca2RuO

4

Insulator: dρ/dT<0 SemiconductorsThe characteristics of semiconductors are between those of insulators and conductorsSilicon and germanium are examples of semiconductors

Polarization Charging by Rubbing

Charging by InductionCoulomb’s Law

r12F q

=ke2q

1212

2 1+q+q F12F21r12

Coulomb’s Law, cont.

ke is called the Coulomb Constantke = 8.99 x 109 N m2/C2

Typical charges can be in the µC rangeRemember, Coulombs must be used in the equation

Remember that force is a vector quantity

Coulomb force Gravitational force

But electric forces may be either attractive or repulsive, whereas gravitational forces are always attractive.

That is why matter in the universe tends to come together to form large bodies, these bodies are always found in groups,

such as galaxies of stars and families of planets. On an atomic scale, electricity is much more important than gravity

r12F m

=G 2m12

12r12F Q

=ke2Q

1212

Example:The hydrogen atom has the simplest structure of all atom, consisting of a proton and an electron whose average separation is 5.3x10-11 m.The mass of electron and proton is 9.1x10-31 kg, 1.67x10-27 kg, respectively

Fe=kQeQp/r2=(9.0x109 N•m/C2)(1.6x10-19 C2)/(5.3x10-11 m)2

=8.2x10-8 NFg=Gmemp/r2

=(6.7x10-11 N•m/kg2)(9.11x10-31 kg)(1.67x10-27 kg)/(5.3x10-11 m)2

=3.7x10-47 Nme=9.11x10-31 kg, mp=1.673x10-27 kg

The electric force is over 10103939 times greater than the gravitational force

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Four point charges, each of the same magnitude, with varying signs are arranged at the corners of a square as shown. Which of the arrows labeled A, B, C, and D gives the correct direction of the net force that acts on the charge at the upper right corner?

a Ab. Bc. Cd. De. The net force on that charge is zero

Answer: b

Question:

QUICK QUIZ 15.2

Object A has a charge of +2 µC, and object B has a charge of +6 µC.

Which statement is true:(a) FAB = –3FBA, (b) FAB = –FBA, or

(c) 3FAB = –FBA

Answer (b)

e = ×19

C1.60 10

Q = ne (n =±0、1、2、3…)

Electric charge always occurs in multiples of e

A conducting sphere has a net charge of −4.8x10−17 C. What is the approximate number of excess electrons on the sphere?

(a) 100 (c) 300 (e) 500

(b) 200 (d) 400

Answer: c (-4.8x10-17 C/-1.6x10-19 C=300 electrons)

Question: Question:Two charges of +Q are 1 cm apart. If one of the charges is replaced by a charge of –Q, the magnitude of the force between them is

(a) zero(b) smaller(c) the same (d) larger

Answer: c

Question: A charge of +q is placed 2 cm from a charge of –Q. A second charge of +q is then placed next to the first. The force on the charge of –Q

(a) decreases to half its former magnitude (b) remains the same (c) increases to twice its former magnitude(d) increases to four times its former magnitude

Answer: c

Two positive point charges Q and 2Q are separated by a distance R. If the charge Q experiences a force of magnitude F when the separation is R, what is the magnitude of the force on the charge 2Q when the separation is 2R ?

(a) F/4 (c) F (e) 4F

(b) F/2 (d) 2F

Question:

Answer: a

Question: Two charges, one positive and the other negative, are initially 2 cm apart and are then pulled away from each other until they are 6 cm apart. The force between them is now smaller by a factor of

(a) 9(b) 3(c) 27(d) √3

Answer: a

Electric Field Electric Field Lines

Outline for Today

Electric Field

Maxwell developed an approach to discussing fieldsAn electric field is said to exist in the region of space around a charged object

When another charged object enters this electric field, the field exerts a force on the second charged object

Electric Field, cont.

A charged particle, with charge Q, produces an electric field in the region of space around itA small test charge, qo, placed in the field, will experience a force

Electric Field

Mathematically,

Use this for the magnitude of the fieldThe electric field is a vector quantityThe direction of the field is defined to be the direction of the electric force that would be exerted on a small positive test charge placed at that point

2e

o rQk

qFE ==

Direction of Electric Field

The electric field produced by a negative charge is directed toward the charge

A positive test charge would be attracted to the negative source charge

Direction of Electric Field, cont

The electric field produced by a positive charge is directed away from the charge

A positive test charge would be repelled from the positive source charge

Electric Field Lines

A convenient aid for visualizing electric field patterns is to draw lines pointing in the direction of the field vector at any pointThese are called electric field lines and were introduced by Michael Faraday

Electric Field Lines, cont.

The field lines are related to the field byThe electric field vector, E, is tangent to the electric field lines at each pointThe number of lines per unit area through a surface perpendicular to the lines is proportional to the strength of the electric field in a given region

Electric Field Line Patterns

Point chargeThe lines radiate equally in all directionsFor a positive source charge, the lines will radiate outward

Electric Field Line Patterns

For a negative source charge, the lines will point inward

Electric Field Line Patterns

An electric dipoleconsists of two equal and opposite chargesThe high density of lines between the charges indicates the strong electric field in this region

Electric Field Line Patterns

Two equal but like point charges At a great distance from the charges, the field would be approximately that of a single charge of 2qThe bulging out of the field lines between the charges indicates the repulsion between the chargesThe low field lines between the charges indicates a weak field in this region

Electric Field Patterns

Unequal and unlike chargesNote that two lines leave the +2q charge for each line that terminates on -q

Question

+ +A

B

C

If a positive test charge is placed at each of the three points,which point experiences the strongest electric field? And which point experience the weakest electric field?

Answer: Strongest at A, weaker at B and zero at C.

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16_26.jpgTwo particles of the same mass carry charges +3Q and –2Q, respectively. They are shot into a region that contains a uniform electric field as shown. The particles have the same initial velocities in the positive x direction. The lines, numbered 1 through 5, indicate possible paths for the particles. If the electric field points in the negative y direction, what will be the resulting paths for these particles?

(a) path 1 for +3Q and path 4 for –2Q

(b) path 3 for +3Q and path 2 for –2Q

(c) path 4 for +3Q and path 3 for –2Q

(d) path 2 for +3Q and path 5 for –2Q

(e) path 5 for +3Q and path 2 for –2Q

Answer: e

Question:

An electron traveling horizontally enters a region where a uniform electric field is directed upward.What is the direction of the force exerted on the electron once it has entered the field?

(a) to the left

(b) to the right

(c) upward

(d) Downward

(e) out of the page, toward the reader

Answer: d

Question:QUICK QUIZ 15.5

A circular ring of radius b has a total charge q uniformly distributed around it. The magnitude of the electric field at the center of the ring is (a) 0 (b) keq/b2 (c) keq2/b2

(d) keq2/b (e) none of these.

QUICK QUIZ 15.5 ANSWER(a). If a test charge is at the center of the ring, the force exerted on the test charge by charge on any small segment of the ring will be balanced by the force exerted by charge on the diametrically opposite segment of the ring. The net force on the test charge, and hence the electric field at this location, must then be zero.

A "free" electron and "free" proton are placed in an identical electric field. Which of the following statements are true? (a)Each particle experiences the same electric force and the same acceleration. (b) The electric force on the proton is greater in magnitude than the force on the electron but in the opposite direction. (c) The electric force on the proton is equal in magnitude to the force on the electron, but in the opposite direction. (d) The magnitude of the acceleration of the electron is greater than that of the proton. (e) Both particles experience the same acceleration.

QUICK QUIZ 15.6

QUICK QUIZ 15.6 ANSWER

(c) and (d). The electron and the proton have equal magnitude charges of opposite signs. The forces exerted on these particles by the electric field have equal magnitude and opposite directions. The electron experiences an acceleration of greater magnitude than does the proton because the electron’s mass is much smaller than that of the proton.

Conductors in Electric Field

The electric field inside a good conductor is zero in the static

situationAny excess charge resides on the

surface of the conductor

Why?

In a conductor electrons are free to move. If a conductor is placed into E, a force F = -eE acts on each free electron. Soon electrons will pile up on the surface on one side of the conductor, while the surface on the other side will be depleted of electrons and have a net positive charge. These separated negative and positive charges on opposing sides of the conductor produce their own electric field, which opposes the external field inside the conductor and modifies the field outside.

Electrons inside the conductor experience no force.

A cavity inside a conductor also is free of electric fieldsA conductor shields its interior from any outside electric fields.Even if there are holes in the surface, the electric field does not penetrate very far. A rule of thumb is that the electric field falls to zero over adistance approximately equal to the diameter of the hole.

Why are you safest inside your car during a thunderstorm?

Question

Answer: E=0 inside the car

In the static situation a conductor has the following properties:

Any excess charge resides on the surface of the conductor

The electric field is zero within the solid part of the conductor

The electric field at the surface of the conductor is perpendicular to the surfaceCharge accumulates and the field is strongest on pointy parts of the conductor

Using Static ElectricityUsing Static Electricity

Photocopiers, Paint Sprayers,

Air ionizers