- #1

nagyn

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## Homework Statement

A solid conducting sphere of radius R and carrying charge +q is embedded in an electrically neutral nonconducting spherical shell of inner radius R and outer radius 2 R . The material of which the shell is made has a dielectric constant of 3.0.

Relative to a potential of zero at infinity, what is the potential at the center of the conducting sphere?

## Homework Equations

V = ∫Edr = kq/r + C

Gauss's law in dielectrics: ∫KEdA = q/ε

_{0}

## The Attempt at a Solution

I've made a few assumptions.

The field in a conducting sphere is zero, which means the potential in a conducting sphere is constant. Looking at just the sphere alone, potential at the center relative to infinity should be kq/R (positive because I'm going against electric field?).

With the dielectric in place to still take zero at infinity I need to take into account the potential difference across the dielectric (I think?)

Edielectric = q/KAε

_{0}

V(R->2R) = -∫Edielectric*dr (negative because I'm going in direction of electric field?) = -kq/Kr [2R - R] = -kq/2KR + kq/KR = kq/2KR

I know that a dielectric will decrease the electric potential, so I thought V = Vsphere - Vdielectric = kq*((1/R) - (1/6R)).

This is not correct and I'm not sure where I messed up.