Q. 40

Expert-verifiedFound in: Page 739

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 .

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

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

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