Q .80 - Excercises And Problems

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### Physics for Scientists and Engineers: A Strategic Approach with Modern Physics

Book edition 4th
Author(s) Randall D. Knight
Pages 1240 pages
ISBN 9780133942651

# Charge is uniformly distributed with charge density \rho inside Calc a very long cylinder of radius R. Find the potential difference between the surface and the axis of the cylinder.

The potential difference between the surface and axis of the cylinder

See the step by step solution

## step 1: given information

Given Info:

Charge is uniformly distributed with charge density \rho inside a very long cylinder of radius R.

Formula Used:

If represents electric field and V represents potential associated with it then they are related by

Gauss's law, E.

Where E

electric field through the surface of area A

charge enclosed by the suiface

Permittivity of vacuum

## step 2: calculation

Consider a Gaussian surface inside the cylinder with radius r

Applying Gauss's law to the Gaussian surface,

gives

So potential difference between the surface and axis of the cylinder is given by,

Therefore,