Electric Potential inbetween Conducting Metal Ball and Thick Shell

1. The problem statement, all variables and given/known data
A conducting metal ball of radius 2m with a charge of 3μC is surrounded by a concentric spherical shell of inner radius 4m and outer radius of 5m with a total charge of 4μC. Determine the electric potential in volts between the ball and shell at a radius of 3m.

2. Relevant equations
V = k∑(q/r)
V = k∫(dq/r)
V = -∫E dA

3. The attempt at a solution

The charge outside of a conductor treats the conductor like a point charge, so…

V = (k(3E-6))/(3) = 9000V

I’m not really sure how to find the voltage inside a spherical shell like this. I think for conductors the potential inside is equal to the potential at the surface, so…

V = (k(4E-6))/(5) = 7200

Vtot = V1 + V2 = 9000V + 7200V = 16200V

But this question came from a practice exam from my professor, and apparently, the answer is actually 14,850V. Where did I go wrong?


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