A particle of positive charge Q is assumed at a point O. A second particle of mass 'm' and negative charge '-q' moves at a constant speed in a circle of radius `r_(1)`, centered at O. The work that must be done by an external agent on the second particle in order to increase the radius of the circle of motion, centered at O to radius `r_(2)` is

Options

A. `W=(Qq)/(4piepsilon_(0))[(1)/(r_(1))-(1)/(r_(2))]`
B. `W=(2Qq)/(piepsilon_(0))[(1)/(r_(1))-(1)/(r_(2))]`
C. `W=(Qq)/(8piepsilon_(0))[(1)/(r_(1))-(1)/(r_(2))]`
D. `W=(4Qq)/(piepsilon_(0))[(1)/(r_(1))-(1)/(r_(2))]`

Answer

C

Explanation

`(Qq)/(4piepsilon_(0)r_(1)^(2))=(mv_(1)^(2))/(r_(1))`
The KE of charge q is,
`KE_(1)=(Qq)/(8piepsilon_(0)r_(1)).........(1)`
Electrical PE of the system, `U_(1)=(-Qq)/(4piepsilon_(0)r_(1))`
`TEimpliesE_(1)=KE_(1)+U_(1)=(-Qq)/(8piepsilon_(0)r_(1)), TEimpliesE_(2)=(-Qq)/(8piepsilon_(0)r_(2)), W=E_(2)-E_(1)=(Qq)/(8piepsilon_(0))[(1)/(r_(1))-(1)/(r_(2))]`