A and B are two spheres of radii a and b. suppose a charge + q is given to the outer sphere B. +q is distributed on its inner an outer surfaces by amounts +q₁ and +q₂ respectively, so that q = q₁ + q₂. The charge + q₁ on the inner surface of B induces a charge –q₁ on the inner surface of B induces a charge – q₁ (bound charge) on the outer surface of A and charge + q₁ on the inner surface of A. being free, leaks to the earth.

The two spheres now behave as two capacitors connected in parallel.

(i) The inner sphere of radius a and the inner surface of outer sphere form a capacitor of capacitance

        C1 = 4πε₀ab    (if the dielectric in air)
                   b – a

(ii) The outer surface of B and the earth form a capacitor of capacitance
        C₂ = 4πε₀ab.

Total capacitance C = C₁ + C₂ = 4πε₀ab + 4πε₀b
                    _________________(b – a)

            C = 4πε₀b²
                     b – a




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