# Electric field of a square's edges

by Niles
Tags: edges, electric, field, square
 P: 1,820 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: http://teacher.pas.rochester.edu/PHY...eworkSet3.html 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: $$\frac{2}{{4\pi \varepsilon }}\int\limits_{x1 }^{x2 } {\frac{\lambda }{{\left( {x^2 + z^2 } \right)}}} \cos \phi dx$$, 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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