Question

Problem 4. An infinite nonconducting sheet is pictured in the Figure below. It has a uniform surface charge density σ. Using Gauß, law on the cylindrical surface depicted below find the electric field E, a distance L/2 above and below the sheet. Reminder: Due to symmetry E is perpendicular to k. L/2 L/2 Problem 4. An infinite nonconducting sheet is pictured in the Figure below. It has a uniform surface charge density ơ. Using Gauß' law on the cylindrical surface depicted below, find the electric field ~ E, a distance L/2 above and below the sheet. Reminder: Due to symmetry~E is perpendicular to k. Please provide an explanation of the solution.

Answer 1

Electric field is along the length of the cylinder, therefore all fluxes will pass through the plane surface of the cylinder or through the ends of cylinder. Due to symmetry, electric filed will be same in magnitude at both the ends as cylinder Total flux passing through cylinder phi = contourintegral E^vector . ds^vector = E x delta s + E x delta s = E x pi a^2 + E x alpha^bar a^2 = 2 E pi^2 partial differential_in in the cylinder partial differential_in = sigma x alpha^bar a^2 Gauss Law contourintegral E^vector . ds^vector = partial differential_in/epsilon_0 = > 2 E x pi a^2 = sigma x alpha^bar a^2/epsilon_0 = > E = sigma/2 epsilon_0 = > E = sigma/2 epsilon_0