Two charges `q_(1)` and `q_(2)` are placed `30 cm` apart, as shown in the figure. A third charge `q_(3)` is moved along the arc of a circle of radius `40 cm` from `C` to `D`. The change in the potential energy o fthe system is `(q_(3))/(4pi epsilon_(0))k`., where `k` is

Options

A. `8 q_(2)`
B. `8 q_(1)`
C. `6 q_(2)`
D. `8q_(1)`

Answer

1

Explanation

`U_(1) = (1)/(4 pi in_(0)) [ (q_(1) q_(3))/(0.4) + (q_(2) q_(3))/(0.5)]`
`U_(2) = (1)/(4 pi in_(0)) [(q_(1) q_(3))/(0.4) + (q_(2) q_(3))/(0.1)]`
`U_(2) - U_(1) = (1)/(4 pi in_(0)) q_(2) q_(3) [ (1)/(0.1) - (1)/(0.5)]`
`= (q_(3))/(4 pi in_(0)) (8q_(2)) = (q_(3))/( 4 pi in_(0)) k`
`k = 8 q_(2)`