A small bead of mass m, carrying a charge q, is constrained to slide along a thin rod of length L. Charges Q?are fixed at each end of the rod (Figure).

(a) Obtain an expression for the electric field due to the two charges Q?as a function of x, where x?is the distance from the midpoint of the rod.

(b) Show that for x?

(c) Show that if q?is of the same sign as Q,?the force that acts on the object of mass m?is always directed toward the center of the rod and is proportional to x.

(d) Find the period of oscillation of the mass m if it is displaced by a small distance from the center of the rod and then released.

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