Consider an assembly of three conducting concentric spherical shells of radii a, b and c as shown in figure. Find the capacitance of the assembly between the points A and B.

These three metallic hollow spheres form two spherical capacitors, which are connected in series.

Solving them individually, for 1) and 2)

For a spherical capacitor formed by two spheres of radii r_o > r_i is given by

C =

Where,

C: Capacitance

r_i: inner radius

r_o: outer radius

k: relative permittivity or dielectric constant

∈: permittivity of space

Similarly,

And

Now, the capacitors are connected in series, net capacitance for series connected capacitors is given by –