Q. 43

Expert-verified
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

# a. Use the methods of Chapter 25 to find the potential at distance on the axis of the charged rod shown in FIGURE P26.43. b. Use the result of part a to find the electric field at distance on the axis of a rod

a. The potential at distance on the axis of the charged rod.

b. The electric field at distance on the axis of a rod .

See the step by step solution

## Part (a) step 1: Given information

We need to find the potential at distance on the axis of the charged rod shown in FIGURE .

## Part (a) step 2: Simplify

The potential in the integral form is given as:

,

where is a dummy variable for the integration and denotes the position at which we calculate the potential. The solution to this integral is

,

Hence, it is

## Part (b) step 1: Given information

We need to find the the electric field at distance on the axis of a rod.

## Part (b) step 2: Simplify

Calculating the electric field strength using part a.

Now, we need to derive the expression we just found. The derivative, according to the constants, will be

After careful derivation, one would obtain

Considering this, the electric field strength will be given by

,

which we can be simplified to