A certain region of space bounded by an imaginary closed...

Name: Problem 67, Chapter 5: Principles of Engineering Physics 1
Uploaded: 2023-02-18T06:37:19-08:00
Duration: 1 min 50 s
Channel: Hubert Agamasu
Description: A certain region of space bounded by an imaginary closed surface (Gaussian surface) contains no charge. Is the electric field intensity always zero everywhere on the surface? If not, under what circumstances is it zero on the surface?

A certain region of space bounded by an imaginary closed surface (Gaussian surface) contains no charge. Is the electric field intensity always zero everywhere on the surface? If not, under what circumstances is it zero on the surface?

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Key Concepts

Gauss's Law

Gauss's Law is a fundamental principle in electromagnetism stating that the net electric flux through any closed surface is proportional to the total electric charge enclosed within that surface. This means that if a Gaussian surface encloses no net charge, the total flux through the surface is zero, but it does not imply that the electric field is zero at every point on the surface.

Electric Field Versus Net Flux

It is important to distinguish between the electric field at a point and the net electric flux through a surface. Zero net flux means that the overall sum of the outward and inward flux contributions is zero, which can occur even if there are nonzero electric field values at various points on the surface. The individual field vectors can be nonzero yet arranged so that their total flux cancels out.

Symmetry and Field Cancellation

The electric field on a Gaussian surface will be zero everywhere only under conditions of high symmetry. Such symmetry might be present in systems where the external fields, if any, are arranged uniformly, leading to a complete cancellation of the field at every point on the surface. Without such symmetry, while the net flux may be zero, the field intensity can be nonzero at specific locations on the surface due to directional variations in the electric field.

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