question_answer

A solid conducting sphere of radius a has a net positive charge 2Q. A concluding 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 charge density on the inner and outer surfaces of the spherical shell will be

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 \[\left( \sigma  \right)=\frac{\text{Charge}}{\text{Surface area}}\] So \[\sigma {{=}_{inner}}=\frac{-2Q}{4\pi {{b}^{2}}}\] And \[\sigma {{=}_{outer}}=\frac{Q}{4\pi {{b}^{2}}}\,\]