Unit: Gauss's Law

Gauss's Law (120 minutes)

• Gauss' Law (SGA) 90 min - students solve for the electric field due to a charged sphere or an infinite cylinder. Emphasis is made on students making symmetry arguments (proof by contradiction) for using Gauss' Law.

Divergence (40 min)

• Definition of divergence (Lecture) 20 min
• Visualizing Divergence (Maple Visualization) 20 min Students practice estimating divergence from graphs of various vector fields.

Divergence Theorem (20 min)

• Reading: GVC § Divergence Theorem
• Derivation of the Divergence Theorem (lecture). We follow “div, grad, curl and all that”, by Schey. The Divergence theorem is almost a lemma based on the definition of divergence. Draw a diagram of an arbitrary volume divided into lots of little cubes. Calculate the sum of all the fluxes out of all the little cubes (isn't this a strange sum to consider!!) and argue that the flux out of one cube is the flux into the adjacent cube unless the cube is on the boundary.

Differential Form of Gauss's Law (10 min)

• Differential Form of Gauss's Law: Maxwell's Eq 1 & 3: $\Vec{\nabla} \cdot \Vec{E} = {\rho \over \epsilon_0}$, $\Vec{\nabla } \cdot \Vec{B} = 0$ (lecture)
• (optional) Divergence of a Coulomb field (requires delta functions) (lecture)
• (optional) Electric field lines (lecture)

Unit: Current, Magnetic Vector Potential, and Magnetic Field

Vector Potentials (Optional)

• Reading: GVC § Magnetic Vector PotentialCurl
• Vector Potential A (lecture) 10 min max This can be just an analogy with electrostatic potential.
• Curl (at least the component definition in rectangular coordinates)

Magnetic Fields

• Derivation of the Biot-Savart Law from Magnetic Vector Potential (lecture) 15 min
• (optional) Comparing B and A for spinning ring (class discussion/lecture)

Unit: Ampère's Law

Stokes' Theorem

• Reading: GVC § Stokes' Theorem
• Derivation of Stokes' Theorem (lecture). We follow “div, grad, curl and all that”, by Schey

Differential Form of Ampère's Law

• Stokes' Theorem (lecture) (Math 3.12: Stokes' Theorem)
• Differential Form of Ampère's Law: Maxwell Eq. 2 & 4 $\Vec{\nabla } \times \Vec{E} = 0$, $\Vec{\nabla } \times \Vec{B} = \mu_0 \Vec{J}$(lecture) (Physics 41: Differential Form of Ampère's Law)

Unit: Conductors

Conductors (1 hr)

• Conductors (lecture)

Unit: Conservative Fields

Conservative Fields

• Conservative Fields (lecture) (Math 3.5: Independence of Path, Math 3.6: Conservative Vector Fields, Math 3.7: Finding Potential Functions)
• Equivalent Statements (lecture)

Unit: Energy

Energy for Continuous Distributions

• Energy for Continuous Distributions (lecture)

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