Question

Three point charges are arranged on a line. Charge q3 = +5.00nC and is at the origin. Charge q2 = -3.50 nC and is at x = 5.00 cm . Charge q1 is at x = 1.50 cm . What is q1 (magnitude and sign) if the net force on q3 is zero?

Answer 1

It is clear from the situation given in the problem that charge q3 is at extreme left followed by q1 in the middle and q2 is in extreme right.

Now to find the magnitude and sign of charge q1, we should know the following two

1. Force between two charges q and q' separated by a distance r is, F = k.q.q'/r^2

Where, k = 9*10^9 N.m^2/C^2

2. Force between two same polarity charge is repulsive and force between two opposite polarity charge is attractive.

Thus according to the question,

Force on q3 by q1 = Force on q3 by q2

=> k.q3.q1/(1.5)^2 = k.q3.q2/(5)^2

=> q1 = q2 * (1.5/5)^2 = 3.5*10^-9*0.09

= 3.15*10^-10 Coulomb

Again from the condition 2 given above for zero force on q3, force exerted by q1 on q3 should be of repulsive nature. As the polarity of q3 is positive, so, polarity of q1 should be positive.