Table of Contents

### Unit: Potentials from Discrete Sources

Some nice review tutorials from Harvey Mudd College

**Hour 1: Electric Potential**- QUIZ
- Coulomb's Law

**Hours 2-3: Potential Due to Point Charges**- Superposition
*Small Group Activity: Visualizing Equipotential Surfaces*

- Equipotential surfaces

**Hour 4: Power Series**This hour is likely to move to Energy and Entropy in the future.- Power Series Approximations
*Small Group Activity: Calculating Coefficients for a Power Series*

- Properties of Power Series

**Hour 5: The Distance between Two Points**- Vectors
*Kinesthetic Activity: Star Trek*

- Dot Products

**Hour 6: Two Point Charges**- Dipoles
*Small Group Activity: Electric Potential for 2 Point Charges (with Power Series)*

**Hour 7: Differential Vector Elements**Math Bits??- The Position Vector
- The
*dr*Vector*Small Group Activity: Vector Differentials*

### Unit: Continuous Charge Distributions

**Hour 8: Line Integrals**Math Bits??- QUIZ
- Line Integrals
*Small Group Activity: Boysenberry Patch*

**Hours 9-10: Integrating Charge Densities**Math Bits??- Charge Density
*Kinesthetic Activity: Acting Out Charge Densities*

- Cross Product
*Small Group Activity: Finding dA and dV*

- Total Charge
*Small Group Activity: Total Charge*

### Unit: Potentials Due to Continuous Distributions

**Hours 11-12: Calculating Potentials**- Find the surface area of a cone
- SQBQ write $d\vec r$ in 3 different coordinate systems
- —— Old ——
- Potential Integrals
*Small Group Activity: The Ring 1 (V)*

- Approximating Integrals with Power Series
- Potential Due to Finite and Infinite Lines

**Hours 13-14: Superposition of Electric Fields**- Electric Field Vectors
*Small Group Activity: The Ring 2 (E)*

### Unit: Derivatives of Fields

**Hour 15-16: Gradient**Math Bits??- QUIZ
- The Gradient
*Surfaces Activity: The Hillside**Small Group Activity: Navigating a Hill**Kinesthetic Activity: Acting out the Gradient*

- Directional Derivatives (Optional)
- Electric Field as Gradient

**Hour 17: Flux**- Electric Flux
*Kinesthetic Activity: The Concept of Flux**Small Group Activity: Calculating Flux**Mathematica Activity: Visualizing Electric Flux*

**Hour 18: Divergence**Math Bits??- The Divergence
*Small Group Activity: Visualizing Divergence*

- The Divergence Theorem
- Gauss's Law (Differential Form)

**Hours 19-20: Gauss's Law**- Gauss's Law (Integral Form)
*Small Group Activity: Using Gauss's Law*

**Hours 21-22: Conservative Fields**- What Fields Are Conservative?
*Small Group Activity: Counting Paths*

- Vector line integrals
- QUIZ
- Relating Work to Potential
*Small Group Activity: Work*

- Finding Potentials from Fields
*Small Group Activity: The Murder Mystery Method*

### Unit: Laplace's Equation

**Hours 23-25: Solving Laplace's Equation**- Second Derivatives
- The Laplacian
- Conductors
- Separation of Variables
*Small Group Activity: Boundary Value Problem*(New activity)*Computer Activity: Relaxation Technique*(Optional/Computation course)

### Unit: Electrostatic Energy

**Hour 26: Energy**- Electrostatic Energy
*Kinesthetic Activity: Energy of Discrete Charges*

### Unit: Current, Magnetic Vector Potential, and Magnetic Field

**Hour 27: Curl**Math Bits??- The Curl as Circulation
*Small Group Activity: Visualizing Curl*

- The Curl in Curvilinear Coordinates

**Hour 28: Current**- Electric Current
- Current Density
*Kinesthetic Activity: Acting Out Current Density*

**Hours 29-30: Vector Potentials**- QUIZ
- What Is Vector Potential?
*Small Group Activity: The Ring 3 (A)*

**Hours 31-32: Magnetic Fields**- The Biot-Savart Law
*Small Group Activity: The Ring 4 (B)*

### Unit: Ampère's Law

**Hour 33: Ampère's Law**- Symmetry Arguments
*Small Group Activity: Ampère's Law*

**Hour 34: Stokes' Theorem**- Curl Revisited
- Stokes' Theorem
*Small Group Activity: Where Is the Current?*We need a new activity

**Hour 35: Review**

## Related Topics Not Currently Included

### Unit: Conductors

#### Step & Delta Functions (1 hr)

Note that this is now covered in Waves and Oscillations, and also in Periodic Systems

- Reading: GVC § Step Functions–The Dirac Delta Function and Densities
- Step Functions
- Delta Functions

#### Boundary Conditions

These feel like they go really well early in the Capstone to set up E and B fields in matter.

#### Product Rules

- Reading: GVC § Product Rules–Integration by Parts
- Product Rules (lecture)
- Integration by Parts (lecture)

#### Energy for Continuous Distributions

- Energy for Continuous Distributions (lecture)