A flat thin non-conducting ring has an inner radius R1 and an outer radius R2 . The disk is uniformly charged with charge per unit area σ(>0) .

Question

(a) What is the electric field at the center, P, of the ring? Express your answer in terms of the following variables, if necessary, R1, R2, σ and the constant ϵ0 (if needed, enter pi for π, epsilon_0 for ϵ0, sigma for σ, R_1 for R1 .. etc).

(b)What is the magnitude of the electric field at point A which is a distance x above the point P? The line AP is perpendicular to the plane of the ring. Express your answer in terms of the following variables, if necessary, R1, R2, σ, x and the constant ϵ0 (if needed, enter pi for π, epsilon_0 for ϵ0, sigma for σ, R_1 for R1 .. etc).

Answer 1

a) 0
b) ((sigma*x)/(2*epsilon_0))*(1/(sqrt(x^2+R_1^2))-1/(sqrt(x^2+R_2^2)))