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Q. 82

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 713

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Short Answer

A hollow cylindrical shell of length L and radius R has charge Q uniformly distributed along its length. What is the electric potential at the center of the cylinder ?

The electric potential is

See the step by step solution

Step by Step Solution

Step 1. Given information and concept used

A hollow cylindrical shell with a radius of R and a length of L has a uniform charge distribution along its length, resulting in a total charge of Q.

The electric potential at a distance r from a point charge q is calculated as follows:

Potential along the central axis of a ring of radius R having charge q, at a distance from the center,

Step 2. Calculate the electric potential in the middle of a charged cylindrical shell. 

Consider a ring with a width of and a distance of x from the cylinder's center. The charge per square meter of cylinder area,

The ring element's charge,

Therefore, the potential at the center of the cylinder due to ring element

As a result of the whole charge distribution, the potential at the cylinder's core,

The potential at the center of the cylinder is found to be

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