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

Answer

A

Explanation

As is clear from Fig, initial potential energy of the system

`U_(1) = (10^(2))/(4pi in_(0)) [(q_(1) q_(2))/(30) + (q_(1) q_(3))/(40) + (q_(2) q_(3))/(50)]`
Find potentail energy of the system `U_(2) = (10^(2))/(4 pi in_(0)) [ (q_(1) q_(3))/(40) + (q_(1) q_(2))/(30) + (q_(2) q_(3))/(10)]`
Change in potentail energy
`U_(2) - U_(1) = (10^(2))/(4 pi in_(0)) [ (q_(2) q_(3))/(10) - (q_(2) q_(3))/(50)]`
`U_(2) - U_(1) = (10^(2))/(4 pi in_(0)) (q_(2) q_(3))/(50) xx4 = (8 q_(2) q_(3))/(4pi in_(0))`
`:. k = 8 q_(2)`