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

Answer

c

Explanation

The potential energy when `q_(3)` is at point C
`U_(1)=(1)/(4piepsilon_(0))[(q_(1)q_(3))/(0.40)+(q_(2)q_(3))/(sqrt((0.40)^(2)+(0.30)^(2)))]`
The potential energy when `q_(3)` is at point D
`DeltaU=U_(2)-U_(1)`
`rArr(q_(3))/(4piepsilon_(0))k=(1)/(4piepsilon_(0))[(q_(1)q_(3))/(0.40)+(q_(2)q_(3))/(0.10)-(q_(1)q_(3))/(0.40)-(q_(2)q_(3))/(0.50)]`
`rArrk=(5q_(2)-q_(2))/(0.50)=(4q_(2))/(0.50)=8q_(2)`.