59. A thin rod of length and uniform charge per unit length A lies along the x axis as shown in Figure P23.69. (a) Show that the electric field at P, a dis- tance y from the rod, along the perpendicular bisec- tor has no x component and is given by E = 2k,A sin 00/y. (b) Using your result to part (a), show that the field of a rod of infinite length is E = 2k,A/y. (Hint: First calculate the field at P due to an element of length dx, which has a charge A dx. Then change variables from x to 0 using the facts that x= y tan 6 and dx = y sec² 0 d0 and integrate over 8.) 0%0 0 dx FIGURE P23.69 70. A charge q of mass Mis free to move along the xaxis. It is in equilibrium: Pair at the origin, midway between a the