Three point charges of `+2muC, -3muC` , and `-3muC` are kept at the vertices A, B, and C, respectively of an equilateral triangle of side 20 cm. what should be the sign and magnitude of the charge (q) to be placed at the midpoint (M) of side BC so that the charge at A remains in equilibrium?

Explanation

Force exerted on charge at A due to charge at B
`F_1=(9xx10^9xx2xx10^(-6)xx3xx10^(-6))/(0.20)^2`=1.35 N
Force exerted on charge at A due to charge at C:
`F_2=(9xx10^9xx2xx10^(-6)xx3xx10^(-6))/(0.20)^2`=1.35 N
`F=sqrt(F_1^2+F_2^2+2F_1F_2 cos 60^@)`
Resultant force ,
`rArr F=sqrt(1.35^2+1.35^2+2xx1.35xx1.35xxcos 60^@)`
`rArr ` F=2.34 N
Net force acts on A along AM, thus charge at M should be positive for charge at A to be at equilibrium.
Let charge at M be q,
`2.34=(9xx10^9xx2xx10^(-6)xxq)/(0.10sqrt3)^2`
`rArr q=3.9xx10^(-6)` C