How to calculate this integral?

[athrun200]

Homework Statement

Homework Equations

The Attempt at a Solution

Can I use this substitution?

 

[hunt_mat]

Looks good, what does it come out to?

 

[athrun200]

Looks good, what does it come out to?

I am not sure for 2 things.

1. Since z is not a constant, does the derivative yield dz?
2. How can I write the range properly?

 

[hunt_mat]

You're fixing a point z and calculating the electric field there, the limits are easy, you have $L=\tan\theta$ and so the upper limit is $\theta =\tan^{-1}L$, the lower on is just 0.

 

[athrun200]

You're fixing a point z and calculating the electric field there, the limits are easy, you have $L=\tan\theta$ and so the upper limit is $\theta \tan^{-1}L$, the lower on is just 0.

Thx!

 

[SammyS]

For your limits of integration look at your triangle. (The angle you labeled L is actually θ.) If x = 0, then sin θ = 0 and if x = L, then sin θ = L/√(L²+z²) .