### Unit: Potentials from Discrete Sources

• QUIZ
• Coulomb's Law
• 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
• Vectors
• Kinesthetic Activity: Star Trek
• Dot Products
• 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
• Electric Field Vectors
• Small Group Activity: The Ring 2 (E)

### Unit: Derivatives of Fields

• QUIZ
• Surfaces Activity: The Hillside
• Small Group Activity: Navigating a Hill
• Kinesthetic Activity: Acting out the Gradient
• Directional Derivatives (Optional)
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

• 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

#### Boundary Conditions

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

#### Energy for Continuous Distributions

• Energy for Continuous Distributions (lecture)

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