Q. 40

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Found in: Page 739

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

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

# An infinitely long cylinder of radius has linear charge density . The potential on the surface of the cylinder is, and the electric field outside the cylinder is . Find the potential relative to the surface at a point that is distance r from the axis, assuming .

The potential relative to the surface at a point that is distance from the axis is .

See the step by step solution

## Step 1: Given information

We have given that the potential on the surface of the cylinder is , and the electric field outside the cylinder is .

We need to find the the potential relative to the surface at a point that is distance from the axis, assuming

## Step 2: Simplify

The potential difference is given as in relation to the electric field strength and the displacement as

where, is the path. Only we have one dimension, the length from the cylinder, which means that we only need to consider the parameter .That is,

The simple formula for potential difference is

Therefore, the potential we have to find is

,

which, after substituting the expressions we know, becomes

.

Solving the integration part

Hence, the potential is