Electric Field & Potential: Please provide detailed solution, with step by step.

Question

Electric Field & Potential:

Please provide detailed solution, with step by step. Preferentially done on computer or on a paper and scanned. I will rate immediately if correct and accurate.

It is 1 of a 4 sub-part question -

Problem 5 - Electric field & potential (25 pts) We assume that atoms can be modeled by considering a spherical negative charge distribution p(r) extending beyond the radial distance a (a > 0), around the nucleus of charge q (q > 0). At distance r from the center O of the atom, the electric potential is given by the following expression: V(r)= q/4pi e0r e^-r/a a) Determine the direction and magnitude of the electric field E(r) created by this charge distribution at a distance r from the origin.

Explanation / Answer

Note that

E(r) = -dV/dr

Thus,

E(r) = [q / (4 pi Eo r)][1/r + 1/a] exp(-r/a) r^

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