A line charge of density (rho)l [C/m] is in the form of a semicircle of radius a lying on the x-y plane with its center located at the origin. The semicircle starts at (phi)= pie / 2 and ends at phi = 3(pie) / 2 in cylindrical coordinates. Find the electric field vector E at the origin for the cases in which
(a) the line charge density (rho)l = (rho)l0 is a constant, and
(b) the line charge density varies along the semicircular ring as (rho)l = A cos(phi).