Two point charge `q_A " and " q_B` are placed in a uniform external electric field `vecE` at point A and B respectively. The position vector of A is `vecr_A` and that of B is `vecr_B . " if " V(vecr_A) " and " V(vecr_B)` be the electric potentials at point A and B due to the external electric field `vecE`, then potential energy of the system will be

Options

A. `q_AV(vecr_A)+ q_BV(vecr_B)`
B. `q_BV(vecr_A)+q_AV(vecr_B)`
C. `q_AV(vecr_A)+q_BV(vecr_B) +(q_Aq_B)/(4piepsi_0|vecr_(AB)|)`
D. `q_BV(vecr_A)+q_AV(vecr_B) +(q_Aq_B)/(4piepsi_0|vecr_(AB)|)`

Answer

C

Explanation

`U=qV " and " U_(12) = (q_1q_2)/(4piepsi_0r)`
`q_(A)V(vecr_A)+q_(B)V(vecr_B) +(q_Aq_B)/(4piepsi_0|vecr_(AB)|)`