Question

Three fixed beads are secured along the y-axis, with a bead of charge +nq at the origin and charges of −mq a distance a above and below the origin. The values of m and n can be set by an operator. On an insulating wire laid along the x-axis, a movable bead with charge −pq is placed. By adjusting m and n, the movable bead can be moved to different equilibrium positions x along the wire. Your supervisor asks you to set up the system and test it. In particular, he asks for answers to the following questions. a)If n = 9 in a particular test, what is the value of m that will place the movable bead in equilibrium at x = a? b) In a second test with n = 9, what is the value of m that will place the movable bead in equilibrium at x = 2a? c) If n = 9 and the largest you can make m is m = 19, what is the closest equilibrium position of the bead to the origin? (Give your answer in terms of a.)

Answer 1

Ans. The net force on the movable bead is zero. Since the force due to +nq is along the x-axis, so the y component of the electric force due to both -mq must cancel out.

We use the Coulomb's law and superposition principle to write the net force on the movable bead when it is at distance x from the origin.