Point charges `q_1` and `q_2` lie o the x-axis at points `x=-a` and `x=+a` respectively.
a. How must `q_1` and `q_2` be related for the net electrostatic force on point charge `+Q`, placed at `x=+a/2, ` to be zero?
b. With the same point charge `+Q` now placed ate `x=+3a//2`

Answer

A, B

Explanation

a.
`q_1 and q_2` shoud be of same sign.
Further `(Kq_1Q)/((3a//2)^2)=(Kq_2Q)/((a//2)^2)`
`:. q_1=9q_2`
b.
Therefore `q_1 and q_2` should be of opposite signs. Furgher,
`(kq_1Q)/((5a//2)^2)=(kq_2Q)/((a//2)^2)`
or magnitude wise `q_1=25q_2` with sign
`q_1=-25q_2`