4.
A semicircular arc (the left half of a circle) or radius R is divided into two uniformly charged quarter
circles with opposite charges +q on the upper part and -q on the lower. The configuration is illustrated
below. We want to use two different methods to find the electric field at the center of the arc (point
P).
+q
R
P
-9
to negative y direction
a) Using a symmetry argument, find the direction of the electric field $\vec{E}$ at point P.
b) Find the electric field by doing an integral, using symmetry to simplify the calculation. As in the last
part of problem 3, you might want to set up x and y axes and use an angle relative to the horizontal
(x) axis as your integration variable.
