(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A metal sphere with radius r_a is supported on an insulating stand at the center of a hollow, metal spherical shell with radius r_b. There is charge +q on the inner sphere and charge -q on the outer spherical shell. Take the potential V to be zero when the distance r from the center of the spheres is infinite.

What is the equation V(r) that models the potential in the region r_a < r < r_b?

2. Relevant equations

ΔV = -∫E(r)∂r

ψ=Q/ε_0

E∫A = ψ; ∫A = 4πr^2

3. The attempt at a solution

1. V(∞) - V(r) = ∫E(r)∂r (from ∞ to r) = ∫E(r)∂r (from ∞ to r_b) + ∫E(r)∂r (from r_b to r);

2. ∫E(r)∂r (from ∞ to r_b) should evaluate to a constant since E(r) = 0 by Gauss' Law (Taking the Gaussian object to have r > r_b, the enclosed charge is -q + q = 0; Electric flux = 0 and therefore electrical field outside the r_b shell is 0.)

3. ∫E(r)∂r (from ∞ to r) = Constant + ∫E(r)∂r (from r_b to r)

4. ∫E(r)∂r (from r_b to r) evaluates to q/(ε_0*4*π)| (from r_b to r)

V(r_a< r < r_b) = q/(ε_0*4*π)| (from r_b to r) is as far as I got.

Did I make a wrong assumption?

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# Homework Help: Finding equation for potential between concentric charged spheres

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