# Gauss's Law

## Gauss's Law

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Calculating the flux through a sphere around a point charge, leading to the statement of Gauss's Law that flux through a closed surface is proportional to the net charge enclosed by the surface.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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Gauss's Law defined; electric flux; open and closed surfaces; choosing gaussian surfaces and examples with spherical, cylindrical, and planar symmetry.

Gauss's Law defined; introduction to Gaussian sufaces for multiple shapes; worked examples for an infinite rod, infinite plane, spherical shell, and solid sphere of uniform charge.

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Restatement; application to sphere of charge, shell of charge, plane of charge.

## Gauss's Law With Spherical Symmetry

Need symmetric situations to find electric field using Gauss's Law. Example of finding the electric field inside and outside a hollow sphere with uniformly distributed charge. Comparison to gravitational field.

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• Watch {}video clip from Lecture 3 (12:50 - 23:43)

## Gauss's Law With Planar Symmetry

Finding the electric field around a plane with uniformly distributed charge. Result is stated, but some of the work is left to students as an exercise.

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• Watch {}video clip from Lecture 3 (23:43 - 30:05)

## Gauss's Law - Cylindrical Symmetry

Finding the magnitude and direction of the electric field created by a long cylinder with uniform charge density.

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• Watch {}video clip from Lecture 12 (3:03 - 11:47)

## Determining Potential from Gauss's Law

Examples utilizing integrals and Gauss's Law to determine potential of a point charge and solid charged sphere.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Electric Flux

Definition; flux through cylinder and closed surfaces; flux with contained charge; Gauss's Law.

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Introduction to the concept of flux and its application to the electric field; flux through generalized surfaces in 3-D.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Proof of Gauss's Law

Theoretical and experimental verification of Gauss's Law.

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## Divergence

Application of divergence to Gauss's Law; divergence theorem; definition with limits and derivatives; finding E from V.

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## Problem Solving Strategies: Using Gauss' Law

Introduces step-by-step method to determine electric field using Gauss's Law for spheres, infinite planes, and infinite lines of charge.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Finding Field and Charge of a Slab from Potential

Given an expression for the electric potential, determine the electric field, location and charge density of the distribution. Solution is included after problem.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Field of Two Parallel Plates of Charge

Find the electric field everywhere due to two parallel oppositely charged infinite planes. Solution is included after problem.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Electric Flux Through a Square Surface

Find the electric flux due to a point charge through a square surface and through a cube. Solution is included after problem.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Gauss's Law for Gravity

Find the gravitational field inside a spherical mass shell, using Gauss's Law. Solution is included after problem.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Electric Potential of a Solid Sphere

Find the electric potential everywhere due to a uniformly charged sphere using Gauss's Law. Solution is included after problem.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Non-Conducting Solid Sphere with a Cavity

Find the electric field within a spherical cavity in a uniformly charged solid sphere.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Field and Potential of a Non-Uniform Sphere

Find electric field and electric potential everywhere due to a sphere with spherically symmetric non-uniform charge density; also, find total potential energy.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Electric Field of a Charged Slab

Find electric field everywhere due to a charged slab using Gauss's Law.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Electric Potential Energy of a Uniform Sphere

Find the total potential energy of a uniformly charged solid sphere.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Calculating Electric Field from Potential

Given an expression for the electric potential, determine the electric field and the appropriate charge density distribution.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Electric Flux through Surfaces

Determine the sign of electric flux through open and closed surfaces.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Applying Gauss's Law

Determine in what situations Gauss's Law should be utilized.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Quick Gauss's Law Questions

Characterize electric field inside charged spherical shell and inside thick charged slab.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Conceptual Questions on Gauss's Law and Conductors

Questions on the interpretation of Gauss's Law and on charge and potential at conductor surfaces.

• 8.02 Physics II: Electricity and Magnetism, Spring 2007
Prof. John Belcher, Dr. Peter Dourmashkin, Prof. Robert Redwine, Prof. Bruce Knuteson, Prof. Gunther Roland, Prof. Bolek Wyslouch, Dr. Brian Wecht, Prof. Eric Katsavounidis, Prof. Robert Simcoe, Prof. Joseph Formaggio, Andy Neely, Matthew Strafuss, Prof. Eric Hudson, Dr. Sen-Ben Liao

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## Electric Field From Charged Disk

5-part E-field problem; calculating and plotting E-field along z-axis; limiting cases; connection to Coulomb's law.

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## Infinite Charged Sheet

4-part Gauss's law problem; finding E-field in 3 cases; plotting along z-axis.

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## Point Charge in a Hollow Sphere

3-part Gauss's law problem; determining qualitative charge distributions for different locations of the charge.

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## Electric Field From Cylinder

3-part Gauss's law problem; finding radial E-field and potential.

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## Uniform Plane Charge

Drawing and explaining electric field near sheet of charge.

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## Charged Cylinder

4-part problem; finding charge distribution, electric field, and potential for charged cylinder, then again with a dielectric.

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## Charged Sphere Inside a Shell

Finding charge distribution, E-field, and field lines of positive sphere inside negative spherical shell.

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