• # question_answer A spherical capacitor of inner radius$a=1$ cm and outer radius $b=2$ cm is earthed as shown. It can be connected to an isolated metallic sphere of radius$c=1$ cm through a    switch S and a very long conducting wire. If initial charge on inner sphere is $q=30\,\,\mu C,$ the charge on the sphere of radius c, when switch S is closed, will be               A)  $10\,\mu C$               B)  $20\,\mu C$ C)  $25\,\mu C$               D)  $30\,\mu C$

When switch S is closed, the charge on sphere A will be redistributed on A and C in the ratio of their capacitances, $\frac{{{q}_{1}}}{q-{{q}_{1}}}=\frac{4\pi {{\varepsilon }_{0}}\,\left( \frac{ab}{b-a} \right)}{4\pi {{\varepsilon }_{0}}C}$ ${{q}_{1}}=\frac{q\,ab}{ab+bc-ca}$ Taking $q=30\,\mu C$ $a=1\,cm,$     $b=2\,cm,$     $c=1\,cm$ We get, ${{q}_{1}}=20\,\,\mu C$ $\therefore$    $q-{{q}_{1}}=30-20=10\,\mu C$