Problem 3. A thin plastic rod of length L carries charges Q distributed uniformly along its length. (a) Show that the potential on the axis of the rod and at a distance x from its center, where x 1> U2 is given by: . r.' 2 9 \"IL V(x)= . , . mayor. .tLi-Z Take innity as the reference point. (b) Hence, show that the electric eld at the point is given by: E(.\\')- Q 1 11i. 4Ko .1.- _ L- I! 4 (c) An identical rod carrying the same charge distribution is now aligned on the axis of the original one (see gure below). The distance between their nearest ends is d. Show that the repulsive electric force that each rod exerts on the other is: F: 9- 1 111(L+d)_ MrsoL' d(2L+d) (d) What answer will you expect when L > 0? (e) Veri.r that your answer is correct in this limit