Suppose that the charge on the rod in Problem 81 is given by (y) = ay2, where y is the distance from the midpoint of

Suppose that the charge on the rod in Problem 81 is given by λ(y) = ay2, where y is the distance from the midpoint of the rod, and that the total charge on the rod is Q.

(a) Determine the constant a.

(b) Find the force dF that acts on an element of charge λ(y) dy.

(c) Integrate the force obtained in part (b) between –L/2 and L/2 to obtain the total force that acts on the rod.