Spherical Capacitor: Solving Electric Field, Displacement Field & Capacitance

[discoverer02]

I'm stuck on the last part of the following problem:

A spherical capacitor has inner radius R and outer radius 3R, and contains to dielectrics, of permittivities e1, which extends from R to 2R, and e2, which extends from 2R to 3R. Assume charges of +q and -q on the inner and outer surfaces.

a) find E (electric field) and D (displacement field) in each region as functions of r.

b) find the capacitance of the capacitor.

c) what is the surface charge on the e1 dielectric at radius R?

for part a) D = (Einitial)(e) = (kq/r^2)e = q/(4pir^2) for both regions.

and E1 = D/e1 = q/(4e1pir^2)
E2 = D/e2 = q/(4e2pir^2)

for part b) V1 = q/(4piRe1) and V2 = Q(24piRe2)

so C1 = 4piRe1 and C2 = 24piRe2 and Ctotal = 24piRe1e2/(6e2-e1)

Having found all this I don't quite know how to approach part c)

A nudge in the right direction would be greatly appreciated.

Thanks

 

[Doc Al]

Originally posted by discoverer02
A nudge in the right direction would be greatly appreciated.

Apply Gauss's Law.

 

[discoverer02]

Again, the answer was right in front of my face.

Thanks Doc Al for pointing it out.

Up to this point I've used Gauss's Law only to find E, so since I already had E, I didn't think to use it to find Q.

I need to loosen up, open my mind and not be so intimidated when doing these problems.

Thanks again.