Question

A total positive charge is distributed uniformly along a thin, straight rod of length L. The rod lies along the x-axis with its left end at the origin as shown in the figure below, (a) Set up correct integrals with the appropriate limits of integration for the x-component and y-component of the electric field at P. Do not evaluate the integrals here. You must indicate/sketch, on the figure, your dx, r, dg and the corresponding dE and its components dEx and dEy at P to receive full credit (b) Evaluate your integrals and give the net electric field at P If you think one of the components is zero, then explain why it is zero. (c) What is the electric field at P for d > L? Explain.

I'm not sure if ive got these in the correct position. I'm also having trouble with the intregal.

Answer 1

- d de dx aq dĒy = de coso = idą Coo 41 Gu r2 d Ey = 1 dx coso - Unto r2 Ey 1 da coso Turto 82 92 = x² pd ² cose = d r = J 2²+ da wartof Gherare le portal de Ey = 1 haGod L /2²+d2

1 den = de sine - d dx scho uofo r2 Ex = 4 dx sino Jчл. Ү" * = 2+d2bin2 = 3 212+0 2 - sinoer - 2 = / 2 /1 ( و E and ra dx Urto I un 2f Logo None of the component will be zow soo, it will be Ex-o if rod lie symmetrically about! the origin to d>2 Euro) Ey = I AL) y ungod (d) lipaun
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