Embed Size (px)
Citation preview
ElectrostaticsThe study of electric charges
Introduction• Did you ever run a comb through your hair? What do
you notice.• What causes the paper holes to jump onto the comb?• There are electrical forces that are in place due to the
presence of charge on the comb.
The Atom• An atom consists of
various charged and uncharged particles.
• The central region is called the nucleus.
• Protons (+) and neutrons make up the nucleus.
• Electrons (-) move around the nucleus in an orbital path.
Nucleus
NeutronsProtons (+)
Electrons (-)
The Significance of Charge• As mentioned before, protons
are positive and electrons are negative.
• An atom with balanced charges is considered neutral.
• The overall charge can be changed by adding or removing electrons. This makes the atom an ion.
Overall Charge:
(Neutral Atom)(Positive Ion)(Negative Ion)
Add e- Take e-
01 1
Actual Charge of Protons/Electrons
• Recall, charge is measured in Coulombs (C).• Even though protons and electrons are very
small, they still have charge.• Let us use q as a variable for charge.
Electron Proton
191.60 10electronq C 191.60 10protonq C
Sample Problem (Atomic Charge)• A helium atom has a net electric charge
of -8.0x10-19C.
• Is it neutral or an ion?• Are there extra electrons or a shortage of them?• How many extra electrons are there?
– Charge Per e-: -1.60*10-19C
# Net
e
qe
q
19
19
8.0 10#
1.6 10
Ce
C
# 5e
Sample Problem• How many excess electrons are on a ball that
has a charge of q = -4x10-17C?
# Net
e
qe
q
17
19
4.0 10#
1.6 10
Ce
C
# 250e
Sample Problem (Atomic Charge)
• An atom has a net electric charge of 4.8x10-19C.
• Are there extra electrons or a shortage of them?• How many electrons short is this atom?• Draw this atom given it is Boron.
Electric Forces• Charges exert a force on other charges
Like Charges Repel
Opposites Attract
Electrostatic Demo’s
• Tape
• Electroscope
• Pith Balls
How do atoms get charged?
• Work can remove electrons from the atom.– Results in a positively charged atom
• The free Electron can be transferred to another atom.– Results in negatively charged atoms
Coulomb’s Law• The electrostatic force one charged object exerts
on an other
• The force is related to the amount of charge – i.e more charge – more force
• The force is proportional to 1/d2 – i.e. the further apart the charges, the smaller
the force
Coulomb’s Law
Symbol Unit
F Force N
q1 Charge C
q2 Charge C
d Distance m
K constant N m2 / C2
1 2
2
Kq qF
d
Ex. Coulomb’s LawObject A has a charge of 6x10-6C. Object B has a charge of 3x10-6C and is 0.03m away. Calculate the force on A.
1 2
2
Kq qF
d
9 2 2 6 6
2
(9.0 10 / )(6 10 )(3 10 )
(.03 )
x N m C x C x CF
m
180F N
Separating Charge• Charges are balanced in neutral objects.• Work must be done to separate charge (free electrons).• Once charge is separated, it can be used in
experiments.
Separation of Charge• Bring a charge rod near a neutral conductor
• Like charges are repelled
• Un-like charges are attracted
Charge by conduction• A charge rod touches a neutral conductor
• Like charges are repelled and uniformly distribute
Charge by InductionA charge object is placed near neutral conductors
A BA BA BA B
Separation of charge takes placeContact between the conducting sphere is brokenThe charge object is removedThe charges on the spheres redistribute to maximum separationResult: Two spheres charged by induction
Charging by Polarization• Certain substances, such as the one below, have polar
molecules. These molecules have opposite charges at each end.
• Charging by polarization takes place when a charged object is brought near, realigning the molecules in the substance.
Magnification
Conductors and Insulators
• Electrical Conductors are similar to Heat conductors.
• Electrical Conductors allow charge to move easily.
• Electrical Insulators do not allow charge to move easily
Conductors and Insulators• Electrical Conductors all electrons to move
easily.– Metals– Graphite
• Electrical Insulators do not allow electrons to move easily– Glass– Plastic– Rubber
Lightning• Lightning: An electrical discharge
between the clouds and oppositely charged ground.
• Charging by induction occurs during thunderstorms
• The negatively charged cloud induces a positive charge on the ground
Lightning• Average Temperature 30,0000C
– (roughly 5x as hot as the sun)
• Typical charge (q) for lightning 10C to 25C
• How many electrons is this?
Lightning is actually a discharge of static electricity. Charge differences are developed from the friction of dust particles within the cloud.
When the concentration of charges becomes too great, an electrical discharge results
Outlet
Ground
• The earth stores a seemingly infinite amount of charge, both kinds.
• An object is grounded when it is connected to the earth or another large object.
• Electrical devices often have a “ground,” which prevents unwanted charge buildup.
• Grounding is also the principle behind lightning rods.
Grounding
The Electroscope• An electroscope is a device that detects
electrical charge in objects brought near.• Its metallic inner contents, which are usually
neutral, have to be separated from surroundings by some type of insulator.
• There are two metal leaves that hang inside.
• When a charged object is brought near, the leaves separate.
• Charge can also be stored in the electroscope by touching it with the rod.
Leaves
Ex. Coulomb’s Law
The distance that separates electrons in a typical atom is 1.6E-12m. What is the electrostatic force between them?
2
1 2Kq qF
d
9 2 2 19 19
12 2
(9.0 10 / )( 1.6 10 )( 1.6 10 )
(1.6 10 )
x N m C x C x CF
x m
59.0 10F x N
Electro-static ApplicationsElectrostatic filter
Ex. Coulomb’s LawThree charges are aligned as shown. Calculate the force on q2 due to q1.
2
1 2Kq qF
d
9 2 2 4 4
12 2
(9.0 10 / )(6.25 10 )(3.5 10 )
(.15 )
x N m C x C x CF
m
12 87500F N
Electric Charge Positions Scale: 1 Square = 0.05m
q1 q3q2
41
42
43
6.25 10
3.5 10
5.25 10
q x C
q x C
q x C
Ex. Coulomb’s LawThree charges are aligned as shown. Calculate the force on q2 due to q3.
9 2 2 4 4
23 2
(9.0 10 / )(3.5 10 )( 5.25 10 )
(.3 )
x N m C x C x CF
m
23 18375F N
Electric Charge Positions Scale: 1 Square = 0.05m
q1 q3q2
41
42
43
6.25 10
3.5 10
5.25 10
q x C
q x C
q x C
2
1 2Kq qF
d
Ex. Coulomb’s LawThree charges are aligned as shown. Calculate the force on q2 due to q3.
87500 18375net right rightF N
Electric Charge Positions Scale: 1 Square = 0.05m
q1 q3q2
41
42
43
6.25 10
3.5 10
5.25 10
q x C
q x C
q x C
105875net rightF
FNet
Coulomb’s Law in 2-D• To find Fnet with 3 or more charges
• Calculate each Force vector.
• It helps to have a grid system on which to work.
• Use vector addition to find the resultant Fnet
q2 q3
q4
F13
F12
F14
q1
Coulomb’s Law in 2-D (cont.)• Find the net force acting on q1.
• First find the distance between q1 and the others.
• Use the Pythagorean Theorem to find these distances.
q2 q3
q1
CA
B
C
B
A
2 2 2A B C 2 2C A B 2 22 3C
13C
12 13d
The variable C from each triangle’s hypotenuse is the variable d used in the Coulomb’s Law equation.
2 2C A B 2 22 4C 20C
13 20d
1st Triangle 2nd Triangle
Coulomb’s Law in 2-D (cont.)
q2 q3
q1
Charge (C)
q1 3.0 X 10-4
q2 -2.6 X 10-5
q3 7.2 X 10-6
2013
1 212 2
12
kq qF
d
2
2
9 4 5
12 2
9.0 10 3.0 10 2.6 10
13
NmC
C CF
m
12 5.4F N
1 313 2
13
kq qF
d
2
2
9 4 6
13 2
9.0 10 3.0 10 7.2 10
20
NmC
C CF
m
13 0.972F N
F12
F13
Coulomb’s Law in 2-D Sample• Determine the direction of each of the forces prior to
vector addition.
q2 q3
q1
5.4N
0.972N
hypopp
adj
hyp
adj
opp
tanopp
adj
1 2tan4
26.6
1 2tan
3
33.7
26.6 180
206.6
33.7 180
146.3
Quad II Adjust Quad III Adjust
F12 F13
• The remaining task is to use analytical vector addition.
Coulomb’s Law in 2-D SampleMag Ang X Y Q
F12 5.4N 146.3° -4.49 3.00 II
F13 0.972N 206.6° -0.87 -0.44 III
FNet 5.94N 154.5° -5.36 2.56 II12 12 cosxF F
12 5.4 cos 146.3xF N 12 4.49xF N12 12 sinyF F
12 5.4 sin 146.3yF N 12 3.00yF N13 13 cosxF F
13 0.972 cos 206.6xF N 13 0.87xF N13 13 sinyF F
13 0.972 sin 206.6yF N 13 0.44yF N
2 2Net Tot TotF X Y
2 25.36 2.56NetF N N
5.94NetF N
12 13Tot x xX F F 4.49 0.87TotX N N 5.36TotX N
12 13Tot y yY F F
2.56TotY N
tan Tot
Tot
Y
X
1tan Tot
Tot
Y
X
1 2.56
tan5.36
N
N
25.5
25.5 180 154.5 5.94 @154.5NetF N
Quad II Adjust
Conclusion• Electrostatics, the study of the forces between charges
at rest.
I had a dream…
And in it there’s no lightning
Coulomb’s Law in 2-D Sample
Three charges are aligned as shown. Find the net force on q1.
41
42
43
4.5 10
3.2 10
7.3 10
q x C
q x C
q x C
Electric Charge Positions Scale: 1 Square = 0.5
cm
q1 q3
q2
Mag Ang X Y Q
F12 5.4N 146.3° -4.49 3.00 II
F13 0.972N 20.6° -0.87 -0.44 III
FNet 5.94N 154.5° -5.36 2.56 II
End Ch 20
Example: Charge Distribution• What is the total charge of three conducting spheres with
charges of 6q,-1q, and 0q
6 ( 1 ) 0totalq q q q
A6q
B-1q
C0q
5totalq q
Example: Charge Distribution cont.
• What is the final charge distribution if sphere A and B touch?
C0q
A6q
B-1qB2.5q
A2.5q
Example: Charge Distribution cont.
• What is the final charge distribution if sphere B and C touch?
B2.5q
A2.5q
C0qC1.25q
B1.25q
Example: Charge Distribution cont.
• What is the total charge of three conducting spheres
A2.5q
C1.25q
B1.25q
2.5 1.25 1.25totalq q q q
5totalq q
Example: Charge Distribution cont.
• Sphere B is twice as large as sphere A, what will be the charge distribution after they touch?
A5q
B5q
Charge by Conduction• Bring a charge rod near a neutral conductor
• Like charges are repelled
• Un-like charges are attracted
A5q
B-1q
C0q
q2
q3
q1
Scale: 1 square =0.1cm
q1 q3q2
