- Gauss's Law
- Determining Potential from Gauss's Law
- Electric Flux
- Proof of Gauss's Law
- Divergence
- Problem Solving Strategies: Using Gauss' Law
- Finding Field and Charge of a Slab from Potential
- Field of Two Parallel Plates of Charge
- Electric Flux Through a Square Surface
- Gauss's Law for Gravity
- Electric Potential of a Solid Sphere

- Non-Conducting Solid Sphere with a Cavity
- Field and Potential of a Non-Uniform Sphere
- Electric Field of a Charged Slab
- Electric Potential Energy of a Uniform Sphere
- Calculating Electric Field from Potential
- Electric Flux through Surfaces
- Applying Gauss's Law
- Quick Gauss's Law Questions
- Conceptual Questions on Gauss's Law and Conductors
- Uniform Plane Charge
- Charged Sphere Inside a Shell

## 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

**Course Material Related to This Topic:**

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.

- Read chapter 4, pages 3-15 of online textbook

8.022

*Electricity and Magnetism,*Fall 2004

Prof. Gabriella Sciolla

**Course Material Related to This Topic:**

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

## 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

**Course Material Related to This Topic:**

## Electric Flux

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

8.022

*Electricity and Magnetism,*Fall 2004

Prof. Gabriella Sciolla

**Course Material Related to This Topic:**

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

**Course Material Related to This Topic:**

- Read chapter 4, pages 2-3 of online textbook

## Proof of Gauss's Law

Theoretical and experimental verification of Gauss's Law.

8.022

*Electricity and Magnetism,*Fall 2004

Prof. Gabriella Sciolla

**Course Material Related to This Topic:**

## Divergence

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

8.022

*Electricity and Magnetism,*Fall 2004

Prof. Gabriella Sciolla

**Course Material Related to This Topic:**

## 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.

*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

**Course Material Related to This Topic:**

- Read chapter 4, pages 30-1 of online textbook

## 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.

*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

**Course Material Related to This Topic:**

- Complete practice problems on pages 27-9

## 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.

*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

**Course Material Related to This Topic:**

- Complete practice problems on pages 32-3

## 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.

*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

**Course Material Related to This Topic:**

- Complete practice problems on pages 32-5

## Gauss's Law for Gravity

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

*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

**Course Material Related to This Topic:**

- Complete practice problems on page 35

## 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.

*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

**Course Material Related to This Topic:**

- Complete practice problems on pages 35-6

## Non-Conducting Solid Sphere with a Cavity

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

*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

**Course Material Related to This Topic:**

- Complete practice problems on page 37

## 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.

*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

**Course Material Related to This Topic:**

- Complete practice problems on page 38

## Electric Field of a Charged Slab

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

*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

**Course Material Related to This Topic:**

- Complete practice problems on page 38

## Electric Potential Energy of a Uniform Sphere

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

*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

**Course Material Related to This Topic:**

- Complete practice problems on page 39

## Calculating Electric Field from Potential

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

*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

**Course Material Related to This Topic:**

- Complete practice problems on page 39

## Electric Flux through Surfaces

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

*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

**Course Material Related to This Topic:**

- Complete practice problems on pages 9-10

## Applying Gauss's Law

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

*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

**Course Material Related to This Topic:**

- Complete practice problems on page 11

## Quick Gauss's Law Questions

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

*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

**Course Material Related to This Topic:**

- Complete practice problems on pages 12-4

## Conceptual Questions on Gauss's Law and Conductors

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

*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

**Course Material Related to This Topic:**

- Complete practice problems on page 37

## Uniform Plane Charge

Drawing and explaining electric field near sheet of charge.

8.02X

*Physics II: Electricity and Magnetism with an Experimental Focus,*Spring 2005

Dr. Peter Dourmashkin, Prof. Gunther Roland

**Course Material Related to This Topic:**

- Complete practice problem 1
- Check solution to practice problem 1

## Charged Sphere Inside a Shell

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

8.02X

*Physics II: Electricity and Magnetism with an Experimental Focus,*Spring 2005

Dr. Peter Dourmashkin, Prof. Gunther Roland

**Course Material Related to This Topic:**

- Complete exam problem 3
- Check solution to exam problem 3