GAUSS'S LAW TO CHARGE INSULATORS: Gauss's law is useful in determining electric fields when the charge distribution is characterized by a high degree of symmetry. The following examples demonstrate ways of choosing the gaussian surface over which the surface integral can be simplified and the electric field determined. In choosing the surface, we should always take advantage of the symmetry of the charge distribution so that we can remove E from the integral and solve for it. The goal in this type of calculation is to determine a surface that satisfies one or more of the following conditions: 1. The value of the electric field can be argued by symmetry to be constant over the surface. 2. The dot product can be expressed as a simple algebraic product E dA because E and dA are parallel. 3. The dot product is zero because E and dA are perpendiculars.

GAUSS'S LAW TO CHARGE INSULATORS: Gauss's law is useful in determining electric fields when the charge distribution is characterized by a high degree of symmetry. The following examples demonstrate ways of choosing the gaussian surface over which the surface integral can be simplified and the electric field determined. In choosing the surface, we should always take advantage of the symmetry of the charge distribution so that we can remove E from the integral and solve for it. The goal in this type of calculation is to determine a surface that satisfies one or more of the following conditions: 1. The value of the electric field can be argued by symmetry to be constant over the surface. 2. The dot product can be expressed as a simple algebraic product E dA because E and dA are parallel. 3. The dot product is zero because E and dA are perpendiculars.

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter6: Gauss's Law

Section: Chapter Questions

Problem 86AP: Two non-conducting spheres of radii R1 and R2 are uniformly charged with charge densities p1 and p2...

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Discuss the possibility of choosing Gaussian surface other than the sphere.For instance what if you choose the cylindrical surface as a Gaussian surface, is it possible to use Gauss’s law in order to calculate the electric fieldof a charged sphere? Explain your answer in detail.
A sphere of radius R has a charge distribution given by rho(r)=A√r where A is a constant. What is the divergence of the electric field at the point r=R/2? Hint: What is the differential form of Gauss’ law?
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