Let D D be the annular region 2 2 , a

Let $D$ be the annular region
$$-\frac{\pi }{2}\le \theta \le \frac{\pi }{2},a\le r\le b$$
where $b>a>0$. Assume that $D$ has a uniform charge distribution of $\rho$ coulombs per square meter. Let $F$ be the net force on a charged particle of charge $Q$ coulombs located at the origin (by symmetry, $F$ acts along the $x$-axis).
(a) Argue as in Exercise 59 to show that
$$F=k\rho Q{\int }_{\theta =-\pi /2}^{\pi /2}{\int }_{r=a}^b\left(\frac{\cos \theta }{r^2}\right)rdrd\theta$$
(b) Compute $F$.