A solid sphere having uniform charge density `rho` and radius R is shown in figure. A spherical cavity ofradius `(R)/(2)` is made in it. What is the potential at point O?

Options

A. `(11R^(2)p)/(24epsilon_(0))`
B. `(5R^(2)p)/(12epsilon_(0))`
C. `(7pR^(2))/(12epsilon_(0))`
D. `(3R^(2)p)/(2epsilon_(0))`

Answer

B

Explanation

Charge of whole sphere `Q=(4/3 pi R^3)p`
Charge of the cavity `q=4/3 pi (R/2)^2 p=Q/8`, Now `V_0`=[(Vv holesphere )-(V cavity)]
`=3/(8 pi e_0) Q/R =1/(4 pi e_0) ((Q/R))/(R/2)=5/(16 pi e_0) Q/R, 5/(16 pi e_0R) times (4/3 pi R^3 p)=5/12 (R^2p)/e_0`