# Homework Help: A Semi- Infinite Conducting Rod

1. Sep 12, 2010

### dunna

1. The problem statement, all variables and given/known data
25. A semi-infinite nonconducting rod (i.e. infinite in one
direction only) has uniform positive linear charge density
lambda. Show that the electric field at point P makes an
angle of 45 degrees with the rod and that this result is
independent of the distance R. (HINT: Separately find
the parallel and perpendicular (to the rod) components
of the electric field at P, and then compare those
components.)

rod
starts
here
_ +++++++++++++++++++++++++ =====> very long
| |
|
R |
|
| |
- P <== this point is a distance R from the end
of the rod

2. Relevant equations
Coulomb's Law
E= kq/r^2

Q= (lambda)*x and thus dQ=(lambda)*dx (assuming the semi-infinite rod beings at 0 and continues on the x-axis)

3. The attempt at a solution

I drew a diagram and using the problems suggestions I solved for the perpendicular component first which I called dE_y (assuming it ran with the y-axis)
dE= (kdQ)/R^2

Then solving for the "parallel" component, I understand that if the rod truly continues to infinity, the distance between the point and the rod will become negligible and thus the influence by the rod on the point will truly be parallel with the rod itself.

dE_x = dEcos(theta) = (k*lambda*dx*cos(theta))/r^2
= (k*lambda*dx*y_0)/(y_0^2+x^2)^(3/2)

and from here it all becomes convoluted.

Thank you for your time