Chapter 24, Problem 77PQ

A When we find the electric field due to a continuous charge distribution, we imagine slicing that source up into small pieces, finding the electric field produced by the pieces, and then integrating to find the electric field. Let’s see what happens if we break a finite rod up into a small number of finite particles. Figure P24.77 shows a rod of length 2ℓ carrying a uniform charge Q modeled as two particles of charge Q/2. The particles are at the ends of the rod. Find an expression for the electric field at point A located a distance ℓ above the midpoint of the rod using each of two methods:

1. a. modeling the rod with just two particles and
2. b. using the exact expression

   $\stackrel{\to }{E}=\frac{kQ}{y}\frac{1}{\sqrt{{\ell }^2+y^2}}�$

3. c. Compare your results to the exact expression for the rod by finding the ratio of the approximate expression to the exact expression.

FIGURE P24.77 Problems 77 and 78.