# Find the electric field for a thin insulating rod when r L

1. Sep 19, 2009

### rozka

Hello everyone,

On my physics homework, I was told to find an expression for the electric field on the x-axis when r >> L when the E = (2kƛ/L)*[rL/(r^2 - (L^2)/4) + ln((2r-L)/(2r+L))] in the i direction. Basically show that it's a dipole field and that it varies as 1/r^3.

As far as I know, we have ƛ(x) = ƛ_0 (2x/L). The charge density varies from -ƛ_0 to +ƛ_0 to 0 as x varies from -L/2 to +L/2. I'm also told that the point we're taking the electric field from is (r, 0) and in this case, r >> L.

I've tried solving it only to get (2kƛ_0)/r in the i-direction for the field, which isn't correct. This was through a lot of algebraic manipulation and rearranging. The rest of my homework is dependent on me finishing this question, so I'm rather nervous about it.

I'd be grateful for any help I can get on it, thanks!