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Introduction to Electrodynamics
· Problem 3.58
Potentials — David J. Griffiths
Physics · equivalent-surface-charge
Problem
Find the charge density
σ
(
θ
)
\sigma(\theta)
σ
(
θ
)
on the surface of a sphere (radius
R
R
R
) that produces the same electric field, for points exterior to the sphere, as a charge
q
q
q
at the point
a
<
R
a < R
a
<
R
on the
z
z
z
axis.
[
A
n
s
w
e
r
:
q
4
π
R
(
R
2
−
a
2
)
(
R
2
+
a
2
−
2
R
a
cos
θ
)
−
3
/
2
]
\left[Answer: \frac{q}{4\pi R}(R^2 - a^2)(R^2 + a^2 - 2Ra\cos\theta)^{-3/2}\right]
[
A
n
s
w
er
:
4
π
R
q
(
R
2
−
a
2
)
(
R
2
+
a
2
−
2
R
a
cos
θ
)
−
3/2
]
Related theory
Relation Between Surface Energy And Surface Tension
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