Two point charges `+Q` and `-Q_(2)` are placed at A and B respectively . A line of force emanates from `Q_(1)` at an angle `theta` with line joining A and B . At what angle will it terminate at B ?

Explanation

We know that number of emerging lines of force f is proportional to magnitude of the change . The field lines emanating from Q1 are spread out equally in all direction . The number of field lines or flux through cone of half angle `theta` is `(Q_(1))/(4pi)2pi (1- cos theta)`
Similary the number of lines of force terminating on `-Q_(2)` at an angle `phi` is `(Q_(2))/(4pi) 2pi (1- cos phi)` .
The total lines of force emanating from `Q_(1)` is equal to the total lines of froce terminating on `Q_(2)`
`rArr (Q_(1))/(4pi) 2pi(1-cos theta) = (Q_(2))/(4pi)2pi(1-cos phi)`
or `(Q_(1))/(2)(1- cos theta) = (Q_(2))/(2)(1- cos phi)`
`Q_(1) sin^(2) theta // 2 = Q_(2) sin^(2) phi //2`
`rArr phi = 2 sin^(-1){ sqrt((Q_(1))/(Q_(2))) sin theta//2}`