Question

Two spherical conductors A and B of radii a and b (b > a)
are placed concentrically in air. B is given charge +Q and A
is earthed. The equivalent capacitance of the system is
(a) 4πℰ₀ ab/b - a
(b) 4πℰ₀ (a + b)
(c) 4πℰ₀b
(d) 4πℰ₀ (b²/b - a)

Answer 1

• The charge Q given to outer sphere distributes as Q  1 on outside
• Q  2  inside which induces charge −Q   on outside of inner sphere
• +Q  2  on inside of inner sphere which is earthed
• The inside of outer and the inner sphere constituting a spherical condenser having capacitance

         C = 4π∈ ab /b-a

• The outside of the outer constitutes an isolated sphere of capacitance

         C' = 4π∈R = 4π∈b

             C eff = 4π∈ b²/b-a

Answer 2

Answer:

C

Solution :

The charge given to inner sphere will pass to the outer sphere. So, the capacitance of outer sphere will be 4πε0b. (As capacitance due to spherical conductor is 4πε0r, where r is radius of conductor)