$(7)$ A thin rod carries a total charge $Q,$ uniformly distributed along its length $(L).$ Point $P$ lies a distance $R$ from one end, in line with the rod. Show that the electric field at point $P$ is given by

$E_x=\frac{1}{4{}_0}\frac{Q}{R(R+L)}$

$($Note: Some potentially useful integrals are given on the last page.$)$

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