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O
P
10
3.0 10 C
q

= ×
5.4 N/C
0.50 m
r
=
p. 11
The Electric Field due to a Point Charge
Consider a point charge
q
sitting in space. We shall call this charge (the charge that sets up an electric field) the
source charge
. Place a
test charge
q
0
at point P a distance
r
from the source charge. Remember that the
test
charge
is always
positive.
The
source charge
can be either positive
or
negatively charged. An electrostatic force
F
acts on the test charge; this force can be computed using Coulomb’s law:
0
2
qq
F
k
r
=
The electric field at P is given by
0
F
E
q
=
. Hence we can write
2
q
E
k
r
=
.
Note that q
0
cancels from the equation
for E.
Ex. Consider the table top of the previous examples. We assume the environment is the same as before, so at
point P there is an electric field of 5.4 N/C directed upward. Now we place a small charge
10
3.0 10
C
q

=
×
at
point O 0.50 m to the left of P. Find the magnitude and direction of the resultant electric field at P.
At point P:
(
29
y
2
10
9
x
x
2
2
2
x
E
5.4 N/C
N m
3.0 10
C
E
;
E
8.99 10
C
0.50 m
E
11 N/C
q
k
r

=
⋅
×
=
=
×
⋅
=
(
29
(
29
2
2
1
1
E=
11 N/C
5.4 N/C
E=12 N/C
E
5.4 N/C
Tan
;
=Tan
=26
E
11 N/C
y
x


+
θ =
θ
θ
°
E = 12 N/C at 26
°
above the +
x
axis.
The fact that we can “overlay” one electric field with another and obtain the resultant electric field using vector
addition is called
the principle of superposition
. Electric and magnetic fields obey the principle of
q
q
0
r
F
P
E
y
E
x
E
y
E
x
E
θ
Rev. 1/22/10
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superposition. Not all fields, however, obey this principle. Strong gravitational fields (such as those near a black
hole), for example, do not obey the principle of superposition. Weak gravitational fields (such as Earth’s), on
the other hand, obey the principle of superposition to a good approximation.
Permittivity of Free Space
It is common practice to express the constant
k
that appears in Coulomb’s law in terms of another constant,
0
ε
(epsilon zero):
0
1
4
k
=
πε
.
0
ε
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 Spring '09
 IRENEPOLYCARPOU
 Charge

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