question_answer

Capacity of a spherical capacitor is \[\frac{25\lambda }{(\mu -1)}\], when inner sphere is charged and outer sphere is earthed and \[{{v}_{P}}=0,\,\,{{v}_{Q}}=v\] when inner sphere is earthed and outer sphere is charged. Then \[{{v}_{P}}=v,\,\,{{v}_{Q}}=0\] is (Assume a = radius of inner sphere and b = radius of outer sphere)

A)  \[{{v}_{P}}={{v}_{Q}}=0\]                                           

B)  \[{{v}_{P}}=0,{{v}_{Q}}=2v\]

C)  \[\eta \]                             

D)  \[\lambda \]

Correct Answer: A

Solution :

                (a.)When outer sphere B is earthed only \[{{C}_{net}}={{C}_{1}}=\frac{4\pi {{\varepsilon }_{0}}ab}{b-a}\] When inner sphere is earthed, there will be two capacitors                                 \[{{C}_{2}}={{C}_{1}}+{{C}_{1}}=\frac{4\pi {{\varepsilon }_{0}}ab}{b-a}+4\pi {{\varepsilon }_{0}}b\]                                 \[=\frac{4\pi {{\varepsilon }_{0}}{{b}^{2}}}{b-a}\]                 \[\Rightarrow \]               \[\frac{{{C}_{1}}}{{{C}_{2}}}=\frac{ab}{{{b}^{2}}}=\frac{a}{b}\]