A ring of radius `R` carries a charge `+q`. A test charge `-q_(0)` is released on its axis at a distance `sqrt(3) R` from its centre. How much kinetic energy will be acquired by the test charge when it reaches at the centre of the ring ?

Options

A. `(1)/(4 pi epsilon_(0)) ((qq_(0))/(R ))`
B. `(1)/(4 pi epsilon_(0)) ((qq_(0))/(2R ))`
C. `(1)/(4 pi epsilon_(0)) ((qq_(0))/(sqrt(3)R ))`
D. `(1)/(4 pi epsilon_(0)) ((qq_(0))/(3R ))`

Answer

2

Explanation

`K_(A) + U_(A) K_(o) + U_(o)`
`K_(A) + (-q_(0))V_(A) = K_(o) + (-q_(0)) V_(o)`
`0 + (-q_(0)) (1)/(4 pi in_(0)) (q)/(2 R) = (1)/(2) mv^(2) + (-q_(0)) .(1)/(4 pi in_(0)) (q)/(R )`
`(1)/(2) mv^(2) = (qq_(0))/(8 pi in_(0) R)`