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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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