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Chapter 26: Q .80 - Excercises And Problems (page 741)

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.

Short Answer

Expert verified

The potential difference between the surface and axis of the cylinder

=-蚁m34ey

Step by step solution

01

given information

Given Info:

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

Formula Used:

If E鈫�represents electric field and V represents potential associated with it then they are related by vecE=-鈭�V

Gauss's law, E. A=Qm系0.

Where E鈫�

electric field through the surface of area A

Qmu鈫� charge enclosed by the suiface

系0鈫� Permittivity of vacuum

02

calculation

Consider a Gaussian surface inside the cylinder with radius r

Applying Gauss's law to the Gaussian surface,

-E脳2蟺rl=蟺r2lp系9

givesE=m2ei

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

螖V=-鈭�0REdr=-鈭�0R蚁r2系鈥�dr

Therefore,螖V=-p2系ur2211R=-aN24系p.

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