3. (25 points) As shown in the figure, there are two semicircular
(radius R), insulating rods in the x-y plane. The 'upper' half-circle rod
has uniform linear charge density $-\lambda$, while the 'lower' half-circle rod
has uniform linear charge density $+\lambda$. The goal of this problem is to
determine the electric field vector at $(0, 0, z)$. The x-axis is up, out of
the page.
A) (5 points) How can symmetry simplify the problem? Which
components of the electric field are zero and which are nonzero?
Briefly explain your answer(s).
B) (5 points) Briefly describe in words how you will solve this problem.
C) (15 points) Execute your plan. Make sketches of the problem from other orientations, if that helps
you with setting up the trigonometry, integrals, etc.
