1. Electric field due to a ring with varying charge density P (0,0, 1) (a) A thin circular ring in the xy-plane centered at the origin has radius R and carries a varying charge per unit length A(a) = do[1+cos(2a)] = 210 cos a, where do is a constant and a is the angle counterclockwise from the +x-axis. We will consider the electric field at points on the z-axis. What do you expect the electric field to be at the origin (z = 0)? Explain your reasoning. (b) What do you expect the electric field to be (approximately) on the z-axis far away from the origin (|z| R)? Explain your reasoning. (c) Find a vector expression for E( z), the electric field at any point P on the z-axis, and show that it reduces to your expressions in parts a) and b) in the appropriate limits. (d) At what point(s) on the z-axis does E have the greatest magnitude? (e) Arrive at an approximation for the electric field near the origin (|z| R). What kind of motion would a point charge of charge -Q exhibit if placed near the origin? Explain your