Chapter 24.5, Problem 24.6CE

a. Figure 24.22A shows a rod of length L and radius R with excess positive charge Q. The excess charge is uniformly distributed over the entire outside surface of the rod. Write an expression for the surface charge density σ. Write an expression in terms of σ for the amount of charge dq contained in a small segment of the rod of length dx.

b. Figure 24.22B shows a very narrow rod of length L with excess positive charge Q. The rod is so narrow compared to its length that its radius is negligible and the rod is essentially one-dimensional. The excess charge is uniformly distributed over the length of the rod. Write an expression for the linear charge density λ. Write an expression in terms of λ for the amount of charge dq contained in a small segment of the rod of length dx. Compare your answers with those for part (a). Explain the similarities and differences.