Question

A capacitor is constructed using concentric conducting spheres. The inner sphere has radius a, the outer sphere (a thin-walled shell) has radius b.

1. Show that the capacitance is ab/k(b − a) when the space between the inner and outer spheres is empty. Start with the result from Gauss’s law for the field outside a uniform spherical charge distribution (derive the potenital difference between the spheres).

2. What is the capacitance if a = 0.1 m and b = 0.103 m?

3. What would the capacitance be if we filled the gap with Aluminum Oxide (and again, make a = 0.1 m and b = 0.103)?

Answer 1

see picture:

Delta y = y_a - y_b = integral^b_a E dz = integral^b_a k Q dz/T^2 using radial symmetry i.e, Q(1/a - 1/b), Q - total charge C = Every delta P = Everyie Q (1/a - 1/b) = 1/k(b - a/ab) = antibody(b -a), k = 8,99.10^9 - coulomb constant a = 0, 1m: b = 0,103 m: C = 3, 82.10^-10 F If we filled the gap with Aluminium oxide The capacitance would increase in e times where e - dielectrical permittivity of aluminium oxide