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Consider two concentric spherical conductors, separated by an isolating material with
(absolute) permittivity e. The two conductors have radius R1 and R2, they are put on a
potential V and V2, which leads to a charge +q and –q sitting on them, respectively.
By the problem's spherical symmetry, we see that the charge on each conductor is
distributed uniformly, and that, in spherical coordinates, the electric field between the
two conductors is of the form
E(r) = -E(r) er.
Determine the capacity C using the following steps:
1. Use Gauss's Law in integral form, with N a ball of radius r (R2 < r < R1), to find
an expression for E(r) in terms of q.
2. Calculate AV = Vị – V2 using the formula
- E•dr
Δν
and with C the black line segment indicated on the drawing (parallel with e,).
3. The capacity now follows from C = q/AV.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff258f736-2efe-4abc-a546-b1bd73d984a7%2Fe25ca24c-8878-4c90-85b4-04c434973782%2Feqr8v5q_processed.png&w=3840&q=75)
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