- #1

Reshma

- 749

- 4

__Question:__Find the electirc field a distance '

**z**' above the midpoint of a straight line segment of length 2L, which carries uniform charge [itex]\lambda[/itex]

__Solution:__Let me work out the steps and show you where my problem is(I have avoided showing some of the steps).

The coordinate axis has been set up taking the midpoint of the wire as the origin. Magnitude of the electric field is given by:

[tex] E = \frac{1}{4\pi \epsilon_0} \int_{0}^{L} \frac{2\lambda z}{(z^2 + x^2)^{3/2}} dx[/tex]

HERE, Griffith has not elaborated the evauation of the integral under the bracket and directly given the solution. I have tried my level best to solve it but couldn't suceed. So can someone show me the intermediate steps involved in evaluating the

**integral**:

[tex]\int_{0}^{L}\frac{1}{(z^2 + x^2)^{3/2}} dx[/tex] ([itex]\lambda[/itex] & z are constants)

For your convenience, the final solution is:

[tex]E = \frac{1}{4\pi \epsilon_0} [\frac{2\lambda L}{z\sqrt{z^2 + L^2}}][/tex]