A ring of charge with uniform charge density PL and radius p'a is located in the...

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A ring of charge with uniform charge density PL and radius p'a is located in the x - y plane. (a) Use integration in cylindrical coordinates to find an expression for the electric field at a general point z along the z-axis. Use symmetry and your judgment about the direction of the field to reduce the complexity of the integral. (b) Show that when z is large (z >> a) the field approaches that of point charge with the same total charge as the ring. (c) For a ring with a = 0.01 and PL = 100 nC/m, do a numerical comparisonof the fields using methods (a) and (b) at two locations: z = 0.01 and z = 1.5. What is the percent error in each case? Z E at point z a y A ring of charge with uniform charge density PL and radius p'a is located in the x - y plane. (a) Use integration in cylindrical coordinates to find an expression for the electric field at a general point z along the z-axis. Use symmetry and your judgment about the direction of the field to reduce the complexity of the integral. (b) Show that when z is large (z >> a) the field approaches that of point charge with the same total charge as the ring. (c) For a ring with a = 0.01 and PL = 100 nC/m, do a numerical comparisonof the fields using methods (a) and (b) at two locations: z = 0.01 and z = 1.5. What is the percent error in each case? Z E at point z a y

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