Two particles A and B , each carrying a charge Q , are held fixed with a separation d between them. A particle C having mass m and charge q is kept at the midpoint of the line segment AB . If particle C is displaced through a distance x perpendicular to AB , determine the electric force experienced by it.

Step-by-step solution

Let the positions of particles A and B be at a distance d 2 from the origin on the line connecting them. Particle C is displaced by a distance x along the perpendicular bisector. The distance of particle C from both A and B is r = x^2 + d^2 4 . The magnitude of the electric force exerted by each charge Q on q is F = 1 4 ₀ Qq r^2 . By symmetry, the components of the forces parallel to the line AB are equal and opposite, thus cancelling each other out. The components of the forces perpendicular to AB (along the displ