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