A charge `+Q` at A (see Fig. 3.140) produces electric field `E` and electric potential V at D. If we now put charges `- 3 Q` and `+Q` at B and C, respectively, then the electric field and potential at `D` will be
.

Options

A. E and 0
B. 2 E and - V
C. `sqrt(2) E and V/(sqrt(2))`
D. 2 E and V

Answer

b

Explanation

When only `+Q` charge is placed at point `A`, electric field at `D` is
`E = (1)/(4 pi epsilon_0) Q/(a^2)` (i)

Electric potential at `D` is
`V = (1)/(4 pi epsilon_0) Q/a` (ii)
When charges `-3 Q` and `+Q` are placed at B and C, respectively, from figure it is clear that electric field at `D` will be `2 E` toward `B`.

Electric potential at `D` will be
`V_D = (1)/(4 pi epsilon_0)Q/a - (1)/(4 pi epsilon_0)(3 Q)/a+ (1)/(4 pi epsilon_0) Q/a = (-1)/(4 pi epsilon_0) Q/a = - V`.