Question

A thin ring of radius R in the x − y plane is centered at the coordinate origin, and is charged with linear charge density λ which depends on the polar angle θ as λ(θ) = λ0 sin(θ), where λ0 > 0.

(a) Sketch λ(θ) for θ ∈ [0, 2π].

(b) Before doing any calculations, sketch the E~ x and E~ y vector components of the electric field at the coordinate origin, as well as where (roughly) you expect the total E~ to point. [Hint 1: keep in mind the orientation of the electric field – it points away from positive charges.]

(c) Calculate Ex.

(d) Calculate Ey.

Answer 1