- Gauss's Law
- Gauss's Law With Spherical Symmetry
- Gauss's Law With Planar Symmetry
- Gauss's Law - Cylindrical Symmetry
- 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
- Electric Field From Charged Disk
- Infinite Charged Sheet
- Point Charge in a Hollow Sphere
- Electric Field From Cylinder
- Uniform Plane Charge
- Charged Cylinder
- Charged Sphere Inside a Shell

8.02

*Electricity and Magnetism,*Spring 2002

Prof. Walter Lewin

**Course Material Related to This Topic:**

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.

- Watch video clip from Lecture 3 (7:11 - 12:50)
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.

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.

8.02

*Electricity and Magnetism,*Spring 2002

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Watch video clip from Lecture 3 (12:50 - 23:43)
Gauss's Law With Spherical 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.

8.02

*Electricity and Magnetism,*Spring 2002

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Watch video clip from Lecture 3 (23:43 - 30:05)
Gauss's Law With Planar Symmetry

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

8.02

*Electricity and Magnetism,*Spring 2002

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Watch video clip from Lecture 12 (3:03 - 11:47)
Gauss's Law - Cylindrical Symmetry

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:**

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

Theoretical and experimental verification of Gauss's Law.

8.022

*Electricity and Magnetism,*Fall 2004

Prof. Gabriella Sciolla

**Course Material Related to This Topic:**

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:**

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

8.02

*Electricity and Magnetism,*Spring 2002

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Complete practice problem 4
- Check solution to practice problem 4

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

8.02

*Electricity and Magnetism,*Spring 2002

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Complete practice problem 6
- Check solution to practice problem 6

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

8.02

*Electricity and Magnetism,*Spring 2002

Prof. Walter Lewin

**Course Material Related to This Topic:**

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

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

8.02

*Electricity and Magnetism,*Spring 2002

Prof. Walter Lewin

**Course Material Related to This Topic:**

- Complete practice problem 2
- Check solution to practice problem 2

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

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

8.02

*Electricity and Magnetism,*Spring 2002

Prof. Walter Lewin

**Course Material Related to This Topic:**

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

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