# E & M Spherical Capacitor Problem

Consider the capacitor formed by a conducting sphere with radius R1 surrounded by a concentric conducting spherical shell with inside radius R2 and outside radius R3.

(1) Calculate the potential of the outer shell when charge Q is put on it and the inner shell is grounded.

(2) Calculate the potential of the inner shell when charge Q is put on it and the outer shell is grounded.

(3) Calculate the charge on the outer sphere when it is grounded and the inner sphere is at potential V.

(4) Convert your calculations above into the coefficients of capacitance---a.k.a. the capacitance tensor.

(5) Convert your calculations above into the potential coefficients---a.k.a. the potential tensor.

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#### Solution Preview

There can be some small variety in the definitions of potential and capacitance tensors.

As you have not written the definitions you use, I had to choose some, and chose the potential tensor P to be defined by equation V_i = sum_j P_ij Q_j

and the capacitance tensor as C = inverse of P.

If your ...

#### Solution Summary

Solution sets out the steps to find various things about a spherical shell capacitor, including potential of the shells, charge to the outer sphere and coefficients of capacitance.

Two problems on capacitors

1. Two parallel plates of area 100cm^2 are given charges of equal magnitudes 8.9X10^-7 but opposite signs. The electric field within the dielectric material filling the space between the plates is 1.4X10^6 V/m. (a) Calculate the dielectric constant of the material. (b) Determine the magnitude of the charge induced on each dielectric surface.

2. You are asked to construct a capacitor having a capacitance near 1 nF and a breakdown potential in excess of 10000V. You think of using the sides of a tall Pyrex drinking glass as a dielectric, lining the inside and outside curved surfaces with aluminum foil to act as the plates. The glass is 15cm tall with an inner radius of 3.6cm and an outer radius of 3.8cm. What are the (a) capacitance and (b) breakdown potential of this capacitor?

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