Hard Physics problem please help!!!!(pic included)?

Question

http://i328.photobucket.com/albums/l341/CristyAustin/Scan0001-1-1.gif

what do i do?

Answer 1

Since the electric field inside the conducting sphere is zero, the potential is just a constant, let it equal C.

Outside the conductor and inside the other, you need to integrate.

-int(E-ds) = delta V

So you need to find the electric field first using gauss' law. At any radius from the inner sphere, there is a constant charge of -Q enclosed.

int(E-dA) = q/epsilon

The field is a constant at each radius, so factor out E

E(4*pi*r^2) = -Q/epsilon

E = -Q/(4*pi*r^2*epsilon) at radius r

So now to find the potential, integrate.

-int(E-ds) = delta V

Since the path is in the direction of the field outwards along the sphere, E-ds is just Eds

-int(E ds) = delta V

-int[r1,r1+r2](-Q/(4*pi*r^2*epsilon) dr)

Factor out constants

Q/(4*pi*epsilon) * int[r1,r1+r2](1/r^2 dr) =

Q/(4*pi*epsilon)* -1/r | r1,r1+r2| =

-Q/(4*pi*epsilon) (1/(r1+r2) - 1/r1)

So that added to a constant potential C is the potential inside the outer sphere.

Then for the other part, you know C = Q/delta V

So do the division. The Q cancels out. This simplifies to something around your answer. Make sure I didn't make any mistakes earlier in the problem but I think it's more or less right.