Q. 43

Expert-verifiedFound in: Page 739

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 .

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

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

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

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

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