Question
Asked Oct 8, 2019

It's an electromagnetics problem.

Two concentric spherical shells of radii R1 and R2, with R1<R2, are fixed with the following values of the electrostatic potential:
p(R1, e) P1Cose
and
p(R2, 0) 2
where p1 and p2
are constants and 0 is the usual polar spherical angle. Find the electrostatic potential for:
a) r<R1, inside the inner shell
b) r R2, outside the outer shell
c) R1<r<R2, between the two shells
d) Find the surface charge density o(e) on each of the two shells.
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Two concentric spherical shells of radii R1 and R2, with R1<R2, are fixed with the following values of the electrostatic potential: p(R1, e) P1Cose and p(R2, 0) 2 where p1 and p2 are constants and 0 is the usual polar spherical angle. Find the electrostatic potential for: a) r<R1, inside the inner shell b) r R2, outside the outer shell c) R1<r<R2, between the two shells d) Find the surface charge density o(e) on each of the two shells.

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Expert Answer

Step 1

(a) The potential inside the inner shell is same as that at its surface

Orc(F)= (R,.0)
= cos
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Orc(F)= (R,.0) = cos

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Step 2

(b)

the potential on the surface of the inner shell

¢(R.e)
k(a)
cose
Rcos
R
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¢(R.e) k(a) cose Rcos R

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Step 3

the potential on the surfac...

(R2,e)
+9
RRgcos&
Яв
R
k
k
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(R2,e) +9 RRgcos& Яв R k k

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