Question

There are two concentric conducting spherical shells. The capacity of
system is C when inner sphere is charged and outer is earthed and when
is
inner sphere is earthed and outer sphere is charged. Then ratio
ell
(radius of inner sphere = 20 cm, radius of outer sphere = 60 cm)​

Answer 1

Answer:4/3

Explanation: when the inner sphere is earthed , the capacitance is 4(pi)(Eo)(R2-R1), when the outer sphere is earthed , it is 4pi(Eo)(R1R2)/(R2-R1), these results can be arrived by integrating electric field to obtain potential, and capacitance is q/v

Answer 2

Correct Question:

There are two concentric conducting spherical shells. The capacity of system is C1 when inner sphere is charged and outer is earthed and when is inner sphere is earthed and outer sphere is charged, capacitance is C2. Then ratio of capacitance ?

Calculation:

When outer sphere is earthened and inner is charged:

$C1 \propto \dfrac{(r1)(r2)}{r2 - r1} \: \: \: \: . \: . \: . \: .(1)$

When inner sphere is earthened and outer sphere is charged:

$C2 \propto \dfrac{ {(r2)}^{2} }{r2 - r1} \: \: \: \: . \: . \: . \: .(2)$

Now, required ratio :

$C1 : C2 = \{(r1)(r2) \} : {(r2)}^{2}$

$\implies C1 : C2 = r1 : r2$

$\implies C1 : C2 = 20 : 60$

$\implies C1 : C2 = 1 : 3$

So, required ratio is 1:3.