Dear Tutors,

Please give me a worked out solution for this practice midterm. It's one problem with three parts. thanks!

Problem 1. (20 points) (a) Derive a mathematical expression for the electric field E at a point on the axis, a distance z above the center of a flat circular loop of radius R, which carries a uniform charge per unit length 2. {Simplify and express your answer in terms of the given parameters and fundamental constants} . (5 points). (b) Derive a mathematical expression for the electric field E at a point on the axis, a distance z above the center of a flat circular disk of radius R, which carries a uniform charge per unit area o. {Simplify and express your answer in terms of the given parameters and fundamental constants} . (5 points) iT ..vwineo diet orthi i Whiemm.00Vr eonis rod and to again(c) A solid dielectric cylinder of length L and radius R has a uniform charge per unit volume p. Derive a mathematical expression for the electric field E at a point on the axis of the cylinder, a distance z above the center of the cylinder, and outside the cylinder, i.e., for z > L/2. {Simplify and express your answer in terms of the given parameters and fundamental constants). (10 points)