$(15$ points$)$ A thin glass rod is bent into a semicircle of radius $R=8cm.$ Charge of $-Q$ is uniformly distributed along the top half, and charge of $+Q$ is uniformly distributed along the bottom half. Find the magnitude and direction of the electric field at the center $($ P $)$ of the semicircle for $|Q|=20nC.$ Show all your work and convince the grader that you have not memorized any expression not given on the equation page.