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**1. The problem statement, all variables and given/known data**

Using an electron as a point particle of charge −e inside a positively charged sphere of radius R ≈ 10^(−10) m and total charge +e, find the density ρ(r) of the positive charge for which the electron oscillates harmonically about the center of the sphere assuming that the only interaction involved is electric. Find the angular frequency and its numerical value. Discuss whether this is consistent with the assertion in the previous problem.

**2. Relevant equations/attempt at a solution**

This is on the first homework set of my EM class, and therefore I have few tools I would be comfortable using to attack this. My idea was to relate the force that the positively-charged sphere (perhaps through Coulomb's Law,

*F = k((q*) to the equation of harmonic oscillation,

_{1}q_{2})/r^{2})*F = -kx.*However, I'm uncertain how to move from there. What is the constant in this (if applicable), and how do I determine the angular frequency

*w = √(k/m)*? Also what concerns me is the "density of the positive charge..." I'm completely lost on knowing what that means. Thanks!