Three point charges are arranged as shown in the figure belo

Three point charges are arranged as shown in the figure below. Find the magnitude and direction of the electric force on the particle

q = 5.06 nC at the origin. (Let r₁₂ = 0.310 m.)

Solution

We know that like charges repel each other while unlike charges attract.

Hence, the positive charge will try and repel \'q\' along negative x axis while the negative charge will pull it downwards

Hence, force along x axis = 8.99 x 10^9 x 6 x 10^-9 x 5.06 x 10^-9 / 0.31 x 0.31

Fx = - 2.84 x 10^-6 N

Force along the y axis = 8.99 x 10^9 x 6 x 10^-9 x 3 x 10^-9 / 0.1 x 0.1

Fy = -16.1 x 10^-6 N

Therefore the net force = 16.35 x 10^-6 N

tan = Fy/Fx = 5.67; That is the angle with negative x is = 57.32 degrees

Hence the angle with positive x axis = 180 + 57.32 = 137.32 degrees