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//6epsilon_0 +E`
B. `rhoR//12epsilon_0 - E`
C. `-rhoR//6epsilon_0 +E`
D. `rhoR//12epsilon_0 +E`

Answer

B

Explanation

b. Let us complete the sphere. Electric field due to lower part at
A is equal to electric field due to upper part at 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)/(12epsilon_0) - E`