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Electric Charge and
Electric Field
Electric Charge and Electric Field 16
AP Physics 4
Lecture Notes
� Coulomb’s Law
� The Electric Field
� Field Lines
� Electric Fields and Conductors
Electric Charge and Electric Field 16
Coulomb’s Law
Coulomb’s law:
221
r
QQkF ====
r1Q 2Q
Charge (Q)
Coulombs (C)
1 C = 6.2421 x 1018 e
e = 1.602 x 10−−−−11119 C
Distance (m)
Coulomb’s constant (k)
k = 8.988 x 109 N⋅⋅⋅⋅m2/C2
Force (N)
12F 21F
2112 FFF ========
Electric Charge and Electric Field 16
Coulomb’s Law
Coulomb’s law:
221
o r
πε4
1F ====
r1Q 2Q
oπε4
1k ====
2mN
2C12o 10x 8.85
kπ4
1ε
⋅⋅⋅⋅
−−−−========
Permittivity of free space
221
r
QQkF ====
Electric Charge and Electric Field 16
The force is along the line connecting the charges,
and is attractive if the charges are opposite, and
repulsive if they are the same.
Coulomb’s Law
Electric Charge and Electric Field 16
Vector addition review:
Coulomb’s Law
Two forces acting
on an object
Electric Charge and Electric Field 16
tail-to-tip method
Parallelogram method
Components method
Coulomb’s law strictly applies only to point charges.
Superposition: for multiple point charges, the forces on
each charge from every other charge can be calculated
and then added as vectors.
Coulomb’s Law
1Q2Q
3Q
32F
31F
3Q
32F
31F
netF
Net force on Q3
Electric Charge and Electric Field 16
Two charged dust particles exert a force of .32 N on each
other. What will be the force if they are moved so they
are only one-eighth as far apart?
Problem 16-06
Coulomb’s law is an inverse square law.
( ) N 48.20 32. 64 == NF
Electric Charge and Electric Field 16
A person scuffing her feet on a wool rug on a dry day
accumulates a net charge of −−−−42 µµµµC. How many excess
electrons does she get,
Problem 16-07
By how much does her mass increase?
lectronse 10 x 622.2C 10 x 602.1
electron 1 C 10 x 42 14
196 ====
−−−−−−−−
−−−−−−−−
kg 10 x 389.2e 1
kg 10 x .119e 10 x 622.2 16
3114 −−−−
−−−−
−−−−−−−− ====
Electric Charge and Electric Field 16
Compare the electric force holding the electron in orbit
(r = 0.53 × 10 l0 m) around the proton nucleus of the
hydrogen atom, with the gravitational force between the
same electron and proton.
What is the ratio of these two forces?
Problem 16-08
21
21
221
221
G
E
mGm
QkQ
r
mGmr
QkQ
F
F========
(((( ))))(((( ))))(((( ))))kg10 x .671kg10 x .119/kgmN 10 x .676
C 10 x 602.1 /CmN 10 x .988827312211
219229
−−−−−−−−−−−−
−−−−
⋅⋅⋅⋅
⋅⋅⋅⋅====
3910 x 3.2====
Electric Charge and Electric Field 16
At each corner of a square of
side L there are four point
charges. Determine the force
on the charge 2Q.
Problem 16-16
Q2Q
3Q4QL
(((( )))) (((( )))) (((( ))))2
2
2
2o
22xL
kQ 8284.4222
L
kQ45cos
L2
Q4Q2k
L
QQ2kF ====++++====++++====
(((( )))) (((( )))) (((( ))))2
2
2
2o
22yL
kQ 8284.8226
L
kQ45sin
L2
Q4Q2k
L
Q3Q2kF ====++++====++++====
2
22y
2xQ2
L
kQ 0625.10 FFF ====++++====
Electric Charge and Electric Field 16
A +4.75 µµµµC and a −−−−3.55 µµµµC charge are placed 18.5 cm apart.
Where can a third charge be placed so that it experiences no
net force?
Problem 16-20Q1 Q2
d x
Q
21 FF ====
(((( )))) 22
21
x
QQk
xd
QQk ====
++++
21
2
Qdx
−−−−====
C 10 x 5.3C 10 x .74
C 10 x 5.3cm 5.18x
66
6
−−−−−−−−
−−−−
−−−−==== cm 116====
Electric Charge and Electric Field 16
The Electric Field
The electric field is defined as the force on a test charge
(small positive charge), divided by the charge:
q
FE ====
E E
F F
qEF ==== qEF −−−−====
Electric Charge and Electric Field 16
Electric field of a point charge
+Q ••••
r
q++++
q
FE ====
qr
Qqk
2====
The Electric Field
2r
QkE ====
2r
QqkF ====
Electric Charge and Electric Field 16
The Electric Field
Calculate forces using Coulomb’s law
Add forces vectorially to get result
Draw a diagram; show all charges, with signs,
and electric fields and forces with directions
Problem solving in electrostatics:
Electric Charge and Electric Field 16
A proton is released in a uniform electric field, and it
experiences an electric force of 3.75 × 10−−−−14 N toward
the south. What are the magnitude and direction of the
electric field?
Problem 16-24
+ south
E
F
q
FE ==== N/C 10x 2.34
C 10x 1.602
N 10x 3.75 591
14========
−−−−
−−−−
Electric Charge and Electric Field 16
What are the magnitude and direction of the electric
field at a point midway between a +7.0 µµµµC and a −−−−8.0 µµµµC
charge 8.0 cm apart? Assume no other charges are
nearby.
Problem 16-28
+ -••••
d
q1 q2
E1
E2
21 EEE ++++====
(((( )))) (((( ))))22
21
2d
kq
2d
kqE ++++====
(((( ))))212qq
d
k4E ++++====
(((( ))))(((( ))))
(((( ))))N x10 8.0N x10 7.0m 08.0
m/CN x10 8.9884 662
9−−−−−−−− ++++
⋅⋅⋅⋅====
N/C x10 8.4E 7====
Electric Charge and Electric Field 16
Two point charges, −−−−Q and +2Q, are separated by a distance
of d = 12 cm. The electric field at the point is zero.
How far from −−−−Q is P?
Problem 16-36
+-Q−−−− Q2++++
d = 12 cm
P
x••••
E1E2
21 EE ====
(((( ))))22
21
dx
kQ
x
kQ
++++====
12
1
Qdx
−−−−====
11
1
QQ2
Qdx
−−−−====
12
dx
−−−−====
12
cm 12
−−−−====
cm 29x ====
Electric Charge and Electric Field 16
A proton (m = 1.67 x 10−−−−27 kg) is suspended at rest in a
uniform electric field E. Take into account gravity at the
Earth's surface, and determine E.
Problem 16-54
+q
E
GF
EF GE FF ====
mgqE ====
q
mgE ====
(((( ))))C 10x 602.1
m/s 9.80 kg 10x 67.1E
91
227
−−−−
−−−−====
N/C 10x 02.1E 7−−−−====
Electric Charge and Electric Field 16
The electric field can be represented by field lines. These
lines start on a positive charge and end on a negative
charge.
The Electric Field
Electric Charge and Electric Field 16
The number of field lines starting (ending) on a positive
(negative) charge is proportional to the magnitude of the
charge.
The Electric Field
The electric field is stronger where the field lines are closer
together.
••••A
••••B ••••C
E
E
Electric Charge and Electric Field 16
Electric field of two charges:
The Electric Field
Electric Charge and Electric Field 16
The electric field between two closely spaced, oppositely
charged parallel plates is constant.
The Electric Field
Electric Charge and Electric Field 16
Field Lines
Field lines indicate the direction of the field; the field is
tangent to the line.
The magnitude of the field is proportional to the density
of the lines.
Field lines start on positive charges and end on negative
charges; the number is proportional to the magnitude of
the charge.
Summary of field lines:
Electric Charge and Electric Field 16
Electric Fields and Conductors
When finger is removed
When charged rod is removed
Electrically neutral
Net positive charge
( on outer surface)
Charging by induction:
Electric Charge and Electric Field 16
Electric Fields and Conductors
Electric Charge and Electric Field 16
Electric Fields and Conductors
The electric field is
perpendicular to the
surface of a conductor
The electric field is zero
inside a conductor
Electric Charge and Electric Field 16
Summary
Insulators: nonconductors
Conductors: electrons free to move
C 10x 1.602e 19−−−−====Charge on electron:
Charge is conserved
Two kinds of electric charge – positive and negative
Objects can be charged by conduction or induction
Charge is quantized in units of e
Coulomb’s law:2
11
r
QQkF ====
Electric field is force per unit charge:q
FE ====
Electric Charge and Electric Field 16
A large electroscope is made with
"leaves" that are 78 cm long wires
with tiny 24 g spheres at the ends.
When charged, nearly all the
charge resides on the spheres. If the
wires each make a 30° angle with
the vertical what total charge Q
must have been applied to the
electroscope? Ignore the mass of the
wires.
Problem 16-64
2
Q
2
Q
LL
m m
θθθθ θθθθ
Electric Charge and Electric Field 16
Problem 16-64
TF
mg
EFθ
0mgθcosFF Ty ====−−−−====∑∑∑∑0θsinFFF TEx ====−−−−====∑∑∑∑
ET FθsinF ==== mgθcosFT ====
mgθcosF
FθsinF
T
ET
====
====θtanmgF E ====⇒⇒⇒⇒
(((( ))))θtanmg
d
2Qk
F2
2
E ======== k
θtanmgd2Q ====⇒⇒⇒⇒
(((( ))))(((( ))))(((( ))))
229
o
C/mN 10x 988.8
30tangk 024.0m 78.02Q
⋅⋅⋅⋅==== C 10x 1.6 6−−−−====
Electric Charge and Electric Field 16