Two point charges `+Q_1 and -Q_2`, are placed at A and B respectively. A line of force emanates from `Q_1` at an angle `theta` with the line joining A and B. At what angle will it terminate at B ?

Explanation

We know that number of lines of force emerge is proportional to magnitude of the charge. The field lines emanating from `Q_1`, spread out equally in all directions. The number of field lines or flux through cone of half angle `theta` is `(Q_1)/(4pi ) 2pi (1 - cos theta)`.
Similarly the number of lines of force terminating on `-Q_2` at an angle `phi`  is `(Q_2)/(4 pi) 2 pi (1 - cos phi)`. The total lines of force emanating from `Q_1` is equal to the total lines of force terminating on `Q_2`
`implies (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`
`sin phi//2 = sqrt((Q_1)/(Q_2)) sin theta//2 implies phi = 2 sin^(-1) {sqrt((Q_1)/(Q2)) sin theta//2}`.