A concentric spherical capacitor is charged to Q on the oute

A concentric spherical capacitor is charged to -Q on the outer sphere and +Q on the inner sphere. The inner sphere is solid, with radius=a, while the outer sphere is hollow, with radius=b. Between the two spheres is a vaccum.

a) Find the potential difference between r=a and r=b and thus find the capacitance of this system directly.

Solution

small inner 0
small outer 2nC (same as just single sphere, because large sphere do not produce E inside)
large inner -2nC (because must be E=0 in body of sphere and therefore inner charge compensated)
large outer -4nC

on large sphere potential U2=k*(q1+q2)/ro2 = 9e9*-4e-9/0.08 = -450v
on small sphere potential U1=U2+k*q1*(1/ro1-1/ri2) = -450 + 9e9*2e-9(1/0.04-1/0.06) = -300v
k = 1/(4*pi*e0) = 9e9. ro/ri - outer/inner radius

after connecting both spheres are single conductor, therefore summary charge -4nC become at out surface of large sphere and potential same (-450v) everywhere inside.

? · 5 years ago