Question

A point charge `–q` revolves around a fixed charge `+Q` in elliptical orbit. The minimum ar.d maximum distance of q from Q are `r_1` and `r_2`, respectively. The mass of revolving particle is `Q gt q` and assume no gravitational effects. Find the velocity of q at positions when it is at `r_1` and `r_2` distance from Q.

Answer 1

Correct Answer - A::B
From conservation of mechanical energy and conservation of angular mometum asbout point O, we have

`1/2mv_1^2-1/(4piepsilon_0).(Qq)/r_1=1/2mv_2^2-1/(4piepsilon_0).(Q.q)/r_2`………i
and `mv_1r_1sin90^@=mv_2r_2sin90^@`
or `v_1r_1=v_2r_2`
Solving these two equations we have
`v_1=sqrt((Qqr_2)/(2piepsilon_0mr_1(r_1+r_2))` and `=sqrt((Qqr_2)/(2piepsilon_0mr_2(r_1+r_2))=v_2`