**Question:**Find the electric field at a distance \( L \) directly above an infinitely large plane carrying uniform surface charge density \( \Sigma \).**Explanation:**To solve this problem, we can use the concept of Gauss's Law. Gauss's Law states that the electric flux through a closed surface is proportional to the enclosed electric charge. For an infinite plane with a uniform surface charge density, we consider a Gaussian surface in the shape of a cylinder with its axis perpendicular to the plane.Since the plane is infinitely large, the electric field will be perpendicular to the surface and uniform at any point equidistant from the plane. Using Gauss's Law, it can be shown that the electric field \( E \) at a distance \( L \) from the plane is given by:\[ E = \frac{\Sigma}{2\varepsilon_0} \]where:- \( \Sigma \) is the surface charge density.- \( \varepsilon_0 \) is the permittivity of free space.This result is independent of the distance \( L \), meaning that the electric field is constant at any distance from an infinite plane with a uniform surface charge.

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Find the electric field at a distance L directly above an infinitely large plane carrying uniform surface charge density Σ.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

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Electric Charges and Fields

One of the fundamental properties is the electromagnetic property. Charge cannot be destroyed by any process and this contributes formally to the law of charge conservation.

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