Question

Three charged cylindrical sheets are present in three spaces with σ = 5 at R = 2m, σ = -2 at R = 4m and σ =-3 at R = 5m. Find the flux density at R = 4.5m.

(a) 4/4.5

(b) 3/4.5

(c) 2/4.5

(d) 1/4.5

This question was addressed to me in semester exam.

The doubt is from Applications of Gauss Law topic in division Electrostatic Fields of Electromagnetic Theory

Answer 1

Correct choice is (c) 2/4.5

To explain: The Gaussian cylinder of R = 4.5m encloses sum of charges of two cylinders (R = 2m and R = 4m).

By Gauss law,  ψ = Q

D(2πRL) = σ(2πRL), D(2π X 4.5) = Q1 + Q2 =  σ1(2π X 2) + σ2(2π X 4), here σ1 = 5 and σ2 = -2. We get D = 2/4.5 units.