(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

In a certain region, a charge distribution exists that is spherically symmetric but

non-uniform. When a positive point charge q is located at (r,θ,φ) near this charge

distribution, there is a resulting electric potential energy for the system given by:

U(r,θ,φ) = ρ(naught)a^2q/18ε(naught)(1-3((r/a)^2) + 2((r/a)^3) for r ≤ a

and 0 for r ≥ a

where ρo is a constant having units of C/m^3 (volume charge density) and a is a

constant having units of m. Note that there is no θ or φ dependence here since the

charge distribution is spherically symmetric.

Determine the electric force F

exerted on charge q as a function of its location

(r,θ,φ) for:

a) r ≤ a

b) r > a

Check that the units of your answer make sense. (Show your work.)

2. Relevant equations

F=-∇U

∇U=dU/drr

3. The attempt at a solution'

I derived ∇U=dU/drrfrom the spherical coordinate gradients and since there is no dependance on phi and theta we will just be using thervector.

therefore:

d/drρ(naught)a^2q/18ε(naught)(1-3((r/a)^2) + 2((r/a)^3)r

= 6r(r-a)/a^3r

This is where I don't know what to do, how would I express my answer?

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# Homework Help: Finding force from electric potential energy using gradients.

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