Chapter 7.3, Problem 48E

A charged rod of length L produces an electric field at point P(a, b) given by

$E(P)={\displaystyle {\int }_{-a}^{L-a}\frac{\lambda b}{4\pi {\epsilon }_0{(x^2+b^2)}^{3/2}}}dx$

where λ is the charge density per unit length on the rod and ε₀ is the free space permittivity (see the figure). Evaluate the integral to determine an expression for the electric field E(P).