- #1

Saitama

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## Homework Statement

A conducting sphere of radius ##a## carries an initial charge ##q_o##. It is surrounded by another concentric sphere of radius ##b##. The space between the two spheres is filled with a dielectric of permittivity ##\epsilon## and conductivity ##\sigma##. Find the electrostatic potential energy stored in the system at time ##t##.

## Homework Equations

## The Attempt at a Solution

The electric field at a distance ##r## from the centre of smaller sphere is ##\frac{q_0}{4\pi \epsilon r^2}##. The electrostatic potential energy stored can be calculated by the following integral:

[tex]U=\int \frac{1}{2}\epsilon E^2dV[/tex]

Replacing dV with ##4\pi r^2dr## and solving, I don't get the right answer. Also, I don't see how can I express U in terms of t and ##\sigma##.

Any help is appreciated. Thanks!