Electric field of a square's edges

by Niles
Tags: edges, electric, field, square
Niles is offline
Apr26-08, 09:03 AM
P: 1,863
1. The problem statement, all variables and given/known data
Find the electric field a distance z above the center of a square loop (side s) carrying a uniform line charge λ (see Figure 1) - it's problem 2 on this page:


3. The attempt at a solution

Ok, first I use symmetry, so the horizontal components must cancel for the 4 edges. The vertical component of one edge is given by:

[tex]\frac{2}{{4\pi \varepsilon }}\int\limits_{x1 }^{x2 } {\frac{\lambda }{{\left( {x^2 + z^2 } \right)}}} \cos \phi dx[/tex],

where cos(\phi) = z / sqrt(x^2+z^2) so x1 = s/2 and x2=s/sqrt(2) since these are the minimal and maximal values of x.

Pay attention to that I have multiplied with 2, so we find the one whole edge, not just the half of one edge. I integrate, and multiply it all with 4 to give the correct result.

Am I correct?
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