Chapter 6
The Electric Potential Due to One or More Point Charges
42
6
The Electric Potential Due to One or More Point Charges
The electric potential due to a point charge is given by
r
q
k
=
ϕ
(61)
where
ϕ
is the electric potential due to the point charge,
k
=
2
2
9
C
Nm
10
99
8
×
.
is the Coulomb constant,
q
is the charge of the particle (the source charge, a.k.a. the point charge) causing the electric
field for which the electric potential applies, and,
r
is the distance that the point of interest is from the point charge.
In the case of a nonuniform electric field (such as the electric field due to a point charge), the
electric potential method for calculating the work done on a charged particle is much easier than
direct application of the forcealongthepath times the length of the path.
Suppose, for instance,
a particle of charge
q
′ is fixed at the origin and we need to find the work done by the electric
field of that particle on a victim of charge
q
as the victim moves along the x axis from
x
1
to
x
2
.
We can’t simply calculate the work as
)
(
1
2
x
x
F
−
⋅
even though the force is in the same direction as the displacement, because the force
F
takes on a
different value at every different point on the x axis from
x
=
x
1
to
x
=
x
2
.
So, we need to do an
integral:
dx
F
d
=
W
dx
qE
d
=
W
dx
x
q
k
q
d
2
′
=
W
∫
∫
′
=
2
1
2
x
x
dx
x
q
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 Fall '08
 RABE
 Physics, Charge, Electric Potential, Electric charge, 0 k, 1 w, 0.0560 m, 0.885 cm

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