Coulomb’s Law
You are expected to:
A) Use Coulomb’s law to calculate the electric forces between charges.
B) Calculate the
E
field due to a discrete charge distribution and simple continuous
charge distributions.
C) Know the distinction between the electric force
F
(see eqs. [1], [2] below) and the
E
field.
D) Use Gauss’ law to calculate the
E
field for symmetric continuous charge
distributions.
E) Solve problems that contain concepts from this chapter + some simple concepts
from PHYS101.
1 Coulomb’s Law
According to Coulomb’s Law, the magnitude of the electrostatic force between two
charged particles with charges Q
1
and Q
2
and separated by a distance r is given by:
F
e
=
k
e
Q
1
Q
2
r
2
,
(1)
where k
e
= 9x10
9
N
·
m
2
/C
2
is the Coulomb constant. The unit of charge is taken as a
Coulomb (C). The constant k
e
is also written as k
e
= 1/4πε
o
where the constant ε
o
is called
the permittivity of free space ε
o
= 8.854x10
12
C
2
/ N
·
m
2
. Since force is a vector quantity,
in the vector form Coulomb’s law is expressed as:
F
12
=
k
e
Q
1
Q
2
r
2
r
12
(2)
where
r
12
is a unit vector directed from Q
1
to Q
2
. The electric charge is quantized in units of 1.6
⨯
10

19
C (magnitude of the charge of an electron).
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View Full DocumentProblem Solving:
1.1 Finding force on a given charge due to a discrete charge distribution.
Break up the problem in three parts:
[1]
Direction
: draw the force vectors at a given charge location due to the other given charges
(Remember: like charges repel, unlike charges attract). A welllabeled diagram will be very
helpful.
[2]
Magnitude
: find the magnitude of various force vectors using eq. [1].
[3] after step [2] treat the problem as a vector manipulation problem. The net force
F
on a given
charge due to a discrete charge distribution is simply the
vector
sum of the forces produced by
individual charges in the charge distribution at the location of the charge of your interest.
Study problem 2 below to clarify the points mentioned above.
2 The Efield
The magnitude of the
E
field generated by a charge Q is given by E = kQ/r
2
. The direction of
E
at
a given location is the direction in which a force would be exerted on a unit positive test charge
placed at that location. The
E
field due to a discrete charge distribution is simply the
vector
sum
of the
E
fields produced by individual charges in the charge distribution.
2.1 Finding the Efield at a given location due to a discrete charge distribution.
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 Fall '10
 OlehTretiak
 Charge, Electric charge, Qin

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