Q- A rigid, insulating fiber if fixed vertically. A charge Q_a = -7 µC is fixed to the fiber at some point. A bead with a hole drilled through its center is slipped over the fiber above Q_a and is free to move along the fiber without friction. The mass of the bead is m = 160 g and its charge is Q_b. At equilibrium, the bead floats a distance y_b = 16 cm above the Q_a.

(a) Calculate the charge on the bead.

(b) If the mass of the bead were tripled (m' = 3m), how far above the origin would it now float at equilibrium?

(c) The bead (with original mass m) is removed and its charge altered to Q_c. When placed on the fiber from below Qc, it floats at equilibrium point y_c = -11 cm below the origin. What is this new charge?

Solution: