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Electric Potential: Electric charge surrounded by two spherical shells

  • Thread starter Bryon
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  • #1
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Homework Statement


A point charge q = -8 μC is surrounded by two thick, conducting spherical shells of inner and outer radii
a1 = 0.3 m, a2 = 0.4 m, a3 = 0.7 m, and a4 = 0.8 m respectively. The inner shell is uncharged; the outer
shell has a net charge Q = -10 μC. At this point in the problem, the potential at infinity is unspecified.

(c) V(a2) - V(a3) = ____________________ V

Homework Equations



E = kQ/r^2

Guass’ Law: ϕ= ʃE·dA

V0 = - ʃE·dl

HELP: Identify the equivalent point-charge that gives the same electric fields everywhere in the region a2 < r < a3 as the specified charge distribution.
HELP: Use the electric potential function that corresponds to the equivalent point-charge problem.

The Attempt at a Solution



Electric field of the sphere at a2:
E = k(-8uC)/(.4^2) = -449500 N/C

Im stuck. I figured out the first two problems but I am not sure how to relate the electric field to the potential, and I am not sure how to get the equivalent point charge. I assume I need to use guass' law to find the equivalent point charge but my queastion is do I just use the difference of a2 and a3 for the radius?
 
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Answers and Replies

  • #2
SammyS
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Assuming that the spherical shells are centered at the origin:

What is the electric field a distance r from the origin, where a2 < r < a3 ?

For a2 < r < a3:

[tex]V(r)-V(a_2)=-\int_{a_2}^{\,r}E(r)\,dr\ .[/tex]
 
  • #3
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Ah. So I just integrate from 0.4 to 0.7? I feel stupid sometimes lol.

Va-Vb = - ʃ(kQ/r^2)dr = kQ((1/a)-(1/b))

Thanks for the help by the way!
 

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