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

A point charge Q is imbedded at the center of a uniformly charged spherical distribution of charge Q'= -Q with radius 'a'. Write down the volume charge density for this negatively charged sphere. Calculate the electric field and the potential inside, and outside, the atom.

2. Relevant equations

I'm concerned that I do not have the correct electric field. I believe that the electric field inside the sphere should be zero, but I do not completely understand why. Though I do understand that when the E-field is zero, then the Potential will be constant.

3. The attempt at a solution

For the volume charge density of the the negatively charged sphere:

-Q = rho*volume of the sphere, where rho is the volume charge density

-Q = rho*4/3*pi*a^3

thus rho = -Q/(4/3*pi*a^3)

then to find the E-field of the sphere considering the point charge, Q, and the negatively charged sphere I found the total charge Q(r):

Q(r) = Q + rho * 4/3*pi*r^3 , where r is some arbitrary radius, r could be greater than or less than 'a'

Q(r) = Q + [-Q/(4/3*pi*a^3) * 4/3*pi*r^3

thugs Q(r) = Q - Q(r^3/a^3)

Then for the E-field:

Integrating E*dA = Q(r)/eo; (where eo is the constant epsilon not)

I get E = Q/(4*pi*eo)[1/r^2 - r/a^3] for r>a and then when r<a then E=0 right???

From here I'm pretty sure I can find the potential, (when E is not zero) but I'm just not sure if I have it right. Thank you for your help!

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