Gauss's Law And Its Application Electric Charges and Fields

#8. Applications of Gauss's Law

(1). Electric Field due to infinitely long straight uniformly charged wire

Consider an infinitely long straight wire of charge density λ. Imagine a cylinder of radius ‘r’ and height ‘l’ be the Gaussian surface.

According to Gauss's law,

(2). Electric field due to an infinitely large uniformly charged plane sheet

Consider an infinitely large plane sheet of surface charge density σ . Imagine a cylinder of small area of cross section penetrating the sheet and extending to both sides equally as the Gaussian surface

(3). Electric field due to a spherical shell of charge (hollow sphere) density σ

Consider a shell of radius R and charge density σ. We have to find the electric field at a point distant r from the center of this shell.

Case 1: E.F Outside the shell

Case 2: E.F Inside the shell

According to Gauss's law,

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