question_answer

A solid conducting sphere of radius a has a net positive charge 2Q. A conducting spherical shell of inner radius \[b\] and outer radius c is concentric with the solid sphere and has a net charge ? Q. The surface charge density on the inner and outer surfaces of the spherical shell will be  [AMU 2002]

A)            \[-\frac{2Q}{4\pi {{b}^{2}}},\frac{Q}{4\pi {{c}^{2}}}\]

B)            \[-\frac{Q}{4\pi {{b}^{2}}},\frac{Q}{4\pi {{c}^{2}}}\]

C)            \[0,\frac{Q}{4\pi {{c}^{2}}}\]

D)            None of the above

Correct Answer: A

Solution :

  (a) Surface charge density (s) \[=\frac{\text{Charge}}{\text{Surface area}}\] So \[{{\sigma }_{inner}}=\frac{-2Q}{\,4\pi {{b}^{2}}}\] and \[{{\sigma }_{Outer}}=\frac{Q}{\,4\pi {{c}^{2}}}\]