-22 A thick semicircular ring lies in the xy-plane, centered about the origin as illustrated in the figure on the right. The thick ring has inner radius a/2 and outer radius a. (a) If the ring has a net charge Q uniformly distributed over its surface, find the vector electric field at the origin in terms of k, Q, a, and appropriate unit vectors. (b) Now assume that the ring has a non-uniform charge density given by (r) = r. If the ring has a net charge Q, find the constant in terms of Q and a. Hint: integrate Q = dA over the ring. (c) For the charge distribution in part (b), find the vector electric field at the origin in terms of k, Q, a, and appropriate unit vectors. a x