Question

Particle 1 of charge q1 = 0.96 μC and particle 2 of charge q2 = -3.02 μC, are held at separation L = 10.6 cm on an x axis. If particle 3 of unknown charge q3 is to be located such that the net electrostatic force on it from particles 1 and 2 is zero, what must be the x coordinate of particle 3?

Answer 1

Given q1 = 0.96C, q2 = -3.02C and L = 10.6cm. The charges are on x-axis. Assume that the charge q1 is at origin. Since q1 is positive and q2 is negative, the third charge q3 cannot be placed in between the q1 and q2. It must be placed ouside (nearer to the charge with smaller magnitude) to make the net force zero. So q3 is to the left of q1. Let x be the distance between q3 and q1 and (L+x) be the distance between q3 and q2.

The force acting on q3 due to q1 is given by,

The force acting on q3 due to q2 is given by,

Since net force is zero, these two forces should be equal and opposite. Therefore,

So the diatance of q3 from q1 is 13cm. Since q1 is at origin and q3 is to the left of q1, the x-coordinate of q3 is -13cm