- #1

elizabeth9681

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## Homework Statement

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.

## Homework 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.

## 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!