Question

A solid conducting sphere of radius R and carrying charge +q is embedded in an electrically...

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.

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

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Answer #1

As the solid sphere of radius R is conducting, so all of the charge +q will reside on the surface of this sphere and it will act as a spherical shell. Now it is embedded inside a nonconducting spherical shell(inner diameter touching the diameter of the sphere) and outer diameter 2R. Since the shell is non conducting, the charge on the sphere will remain intact and will not be transferred to the outer shell. Therefore, The charge remains at distance R from the center.

So, the potential at the center of the conducting sphere will be equal to the potential due to a spherical shell at center of radius R which is equal to  

q/(40R) which is the required potential.

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