Charge Q is uniformly distributed throughout the volume of a solid hemisphere of radius R metres. Then the potential at centre O of hemisphere in volts is:

Options

A. `( 1)/(4 pi epsi_(0)) (3Q)/(2R)`
B. `(1)/(4 pi espi_(0)) (3Q)/(4R)`
C. `(1)/(4 pi epsi_(0)) (Q)/(4R)`
D. `(1)/(4 pi epsi_(0)) (Q)/(8R)`

Answer

A

Explanation

The potential at centre of sphere in which q charge is uniformly distributed throughout the volume is :
`V_c=1/(4 pi e_0) (3q)/(2R)`
By symmetry, the potential at centre due to half sphere will be half of the complete
`V_c=1/(4 pi e_0) (3q//2)/ (2R)=1/(4 pi e_0) (3Q)/(2R) [ because q/2=Q]`