Two charges `Q_(1)` and `Q_(2)` coulombs are shown in figure. A third charge `Q_(3)` coulombs is moved from points R to S along a circular path. Change in potential energy of the charge is -

Options

A. `kQ_(1)Q_(2)Q_(3)`
B. `4kQ_(1)Q_(2)`
C. `4kQ_(2)Q_(3)`
D. `(2)/(3)kQ_(2)Q_(3)`

Answer

C

Explanation

`U_(i)=(KQ_(1)Q_(3))/(0.8)+(KQ_(2)Q_(3))/(I)+(KQ_(1)Q_(2))/(0.6)`
`U_(f)=(KQ_(1)Q_(3))/(0.8)+(KQ_(2)Q_(3))/(0.2)+(KQ_(1)Q_(2))/(0.6)`
` /_\U=U_(f)-U_(i)=(KQ_(2)Q_(3))/(I)-(KQ_(2)Q_(3))/(0.2)`
`=KQ_(2)Q_(3)(1-(1)/(0.2))`
`|U|=4KQ_(2)Q_(3)`