Chapter19
Coulomb’s Law
You are expected to:
1.
Use Coulomb’s law to calculate the electric forces between charges.
2.
Calculate the
E
field due to a discrete charge distribution and simple continuous
charge distributions.
3.
Know the distinction between the electric force
F
(see eqs.[1], [2] below) and the
E
field
4.
Use Gauss’ law to calculate the
E
field for symmetric continuous charge
distributions.
5.
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:
12
2
e
QQ
Fk
r
=
…[1]
Where
k = 9x10
9
N.m
2
/C
2
is the Coulomb constant. The unit of charge is taken as a
Coulomb (C). The constant
k
is also written as
k = 1/4
πε
o
where the constant
ε
o
is called
the permittivity of free space
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:
12
12
2
ˆ
F
k
r
=
G
r
…[2]
r
+
+
^
r
12
Q
1
Q
2
F
21
F
12
Where
is a unit vector directed from Q
12
ˆ
r
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 Efield 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.
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 Spring '08
 N/A
 Physics, Charge, Force, Electric charge

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