An air-filled spherical capacitor is constructed

Question

with inner and outer shell radii of 6.4 cm and
16.1 cm, respectively.
Calculate the capacitance of the device.
The value of the Coulomb constant is
8.98755 × 10
9 N·m^2/C^2
Answer in units of pF

Answer 1

a is inner , b is outer
a has +q
b has -q inside, +q outside

Voltage of a (integrate E to 0 at infinity
Va = q/(4 pi eo ra)

Voltage of b (same way with q)
Vb = q/(4 pi eo rb)

V = Va-Vb = (q/4 pi eo) (1/ra - 1/rb)
= (q/4 pi eo) (rb-ra)/(ra rb)

C = q/V = 4 pi eo ra rb / (rb-ra)