Figure shows a uniformly charged hemisphere of radius R. It has a volume charge density `rho`. If the electric field at a point 2R, above the its center is E, then what is the electric field at the point 2R below its center?

Options

A. `rhoR//6 epsilon_(0)+E`
B. `rhoR//12 epsilon_(0)-E`
C. `-rhoR//6 epsilon_(0)+E`
D. `rhoR//12 epsilon_(0)+E`

Answer

B

Explanation

Let us complete the sphere. Electric field due lower part at `A=` electric field due to upper part
`B=E` (given)
Electric field due to lower part at `B=` electric field due to full sphere- electric field due to upper part
`(KQ)/((2R)^(2))-E=(1)/(4piepsilon_(0))(rho(4//3)piR^(3))/(4R^(2)) -E=(rhoR)/(12 epsilon_(0))-E`