28. Let E be the electric field due to a long, uniformly charged rod of ra- dius R with charge density 8 per unit length (Figure 21). By symmetry, we may assume that E is everywhere perpendicular to the rod and its mag- nitude E(d) depends only on the distance d to the rod (strictly speaking, this would hold only if the rod were infinite, but it is nearly true if the rod is long enough). Show that E(d) = 8/2re0d for d > R. Hint: Apply Gauss's Law to a cylinder of radius R and of unit length with its axis along the rod. E -R Charged rod FIGURE 21

28. Let E be the electric field due to a long, uniformly charged rod of ra- dius R with charge density 8 per unit length (Figure 21). By symmetry, we may assume that E is everywhere perpendicular to the rod and its mag- nitude E(d) depends only on the distance d to the rod (strictly speaking, this would hold only if the rod were infinite, but it is nearly true if the rod is long enough). Show that E(d) = 8/2re0d for d > R. Hint: Apply Gauss's Law to a cylinder of radius R and of unit length with its axis along the rod. E -R Charged rod FIGURE 21