Chapter 24, Problem 28PQ

The electric field at a point on the perpendicular bisector of a charged rod was calculated as the first example of a continuous charge distribution, resulting in Equation 24.15: $\stackrel{\to }{E}=\frac{kQ}{y}\frac{1}{\sqrt{{\ell }^2+y^2}}\hat{j}$

a. Find an expression for the electric field when the rod is infinitely long.

b. An infinitely long rod with uniform linear charge density λ also contains an infinite amount of charge. Explain why this still produces an electric field near the rod that is finite.