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 . Particle C is displaced through a distance x perpendicular to AB . Assuming x d , which of the following expressions represents the approximate electric force experienced by it?

Step-by-step solution

Let the positions of particles A and B be (- d 2 , 0) and ( d 2 , 0) respectively. The initial position of particle C is (0, 0) . When C is displaced by a distance x perpendicular to AB , its new position is (0, x) . The distance of particle C from both A and B is r = ( d 2 )^2 + x^2 . 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 cancel each other out. The net force is directed along the perpendicular bisecto