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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
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,
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
=
dx
x
q
k
q
d
2
′
=
∫
∫
′
=
2
1
2
x
x
dx
x
q
k
q
d
∫
−
′
=
2
1
2
x
x
dx
x
q
q
k
W
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This note was uploaded on 02/29/2012 for the course PHYS 227 taught by Professor Rabe during the Fall '08 term at Rutgers.
 Fall '08
 RABE
 Physics, Charge, Electric Potential

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