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Date |
Topics |
Reading |
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1 |
1 Sept 2026 |
Vector and tensor transformations; pseudovector, dyads and tensors. Review of vector identities. Vector derivatives: gradient, divergence, curl. Homework #1 assigned. |
1-19
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|
2 |
3 Sept 2026 |
Product rules, second derivatives. The fundamental theorems of calculus for vectors: gradient theorem, Stokes's theorem, and Gauss's divergence theorem. |
20-33
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3 |
8 Sept 2026 |
Vector derivatives in curvilinear coordinates. Dirac delta function. Helmholtz's theorem; scalar and vector potentials. Homework #2 assigned. |
33-53
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4 |
10 Sept 2026 |
Coulomb's Law, units. E as a vector field. E from continuously distributed charges. Example of calculations of E from Coulomb's Law. |
57-69
|
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5 |
15 Sept 2026 |
Gauss's Law. Example E calculations comparing the Gauss and Coulomb laws. Homework #3 assigned. |
69-76
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6 |
17 Sept 2026 |
Curl of E (= 0) in electrostatics. Electric (scalar) potential V, E = - grad V , etc. Curl of E (= 0) in electrostatics. Arbitrariness of reference potential. Superposition. Example calculations of potential. Work and energy; relation to F and V; nonsuperposition. Arbitrariness of reference potential. |
76-81, 88-94
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|
7 |
22 Sept 2026 |
Poisson's and Laplace's equations. Boundary conditions; lightning. Example solution of Poisson's equation in 1-D. Conductors as equipotentials. Forces on conductors. Homework #4 assigned. |
81-88, 95-102, 113-118
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8 |
24 Sept 2026 |
The Lemma: averages, lack of local extrema. Uniqueness of solutions to Poisson and Laplace equations. |
118-123
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9 |
29 Sept 2026 |
Introduction to solution of the Laplace equation by separation of variables. Example in Cartesian coordinates: orthogonality of sines, and Fourier's Trick. Homework #5 assigned.
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129-139
|
|
10 |
1 Oct 2026 |
Solution of Laplace's equation by separation of variables, in spherical coordinates; Legendre polynomials. Example of the pinwheel potential.
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139-147
|
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11 |
6 Oct 2026 |
More separation-of-variables problems, including mixed and complicated boundary conditions. Homework #6 assigned.
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Reread 113-147
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12 |
8 Oct 2026 |
Potential and field from an electric dipole. Solution of Laplace's equation by multipole expansions of the potential.
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147-156
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13 |
15 Oct 2026 |
Calculation of V by method of images. Induced charge on conductors; example of point charge and conducting sphere. Summary of analytical, electrostatic E and V calculation paths; Purcell's Triangle. Homework #7 assigned. |
124-129
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20 Oct 2026 |
Midterm examination, 8:00 AM - 9:15 AM, covering all material introduced so far.
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|
| 14 |
20 Oct 2026 |
Return to the Lemma: the relaxation (finite-element) method for numerical solution of the Laplace equation. Remaining details of multipole moments: origin of coordinates, force, torque. |
Reread 85-88; 115-116, 153-156
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15 |
22 Oct 2026 |
Electric fields in matter: polarizability; induced dipoles; torque on electric dipole in uniform electric field. Polarization vector field P. Bound charge. Electric fields from polarized media. The electric displacement vector field D. Dielectrics and electric susceptibility. Homework #8 assigned.
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166-186
|
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16 |
27 Oct 2026 |
Calculations of E and V for linear dielectrics. Forces and energy in dielectrics; energy density of fields in dielectric media; forces on dielectrics in capacitors. |
186-208
|
|
17 |
29 Oct 2026 |
Begin magnetostatics: Lorentz Force Law; force on a steady current. Current density, continuity equation. The Biot-Savart Law. |
209-223
|
|
18 |
3 Nov 2026 |
Example calculation of magnetic field B from the Biot-Savart Law. Curl of B; derivation, and use, of Ampere's Law. Homework #9 assigned. |
223-232
|
|
19 |
5 Nov 2026 |
Divergence of B; derivation of Gauss's Law of Magnetism. Magnetic monopoles. Proof of the Helmholtz field theorem. The magnetic potential A; the Coulomb gauge. |
232-245, 585-587.
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|
20 |
10 Nov 2026 |
Summary of calculation methods and boundary conditions for magnetostatics. Example calculations of B via Ampere's Law and via A. Homework #10 assigned. |
245-251.
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|
21 |
12 Nov 2026 |
Magnetic multipoles; torque on dipoles; Magnetization vector field M and bound currents; auxiliary magnetic vector field H. Calculation of B and H in linear media. Magnetic susceptibility and permeability, ferromagnetism.
|
251-297
|
|
22 |
17 Nov 2026 |
Begin electrodynamics. Ohm's Law and its microscopic basis. Conductivity. Homework #11 assigned. |
298-304
|
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23 |
19 Nov 2026 |
Motional EMF and magnetic force. |
304-315
|
|
24 |
24 Nov 2026 |
Induction and Faraday's Law. Magnetoquasistatics. Examples of use of Faraday's Law in induced E calculations.
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316-325
|
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25 |
1 Dec 2026 |
Induced E and A. Mutual and self inductance. Use of inductance to calculate fields. Homework #12 assigned |
325-330
|
|
26 |
3 Dec 2026 |
Energy in magnetic fields. Displacement current, and the finishing touches to the Maxwell equations.
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331-345
|
|
27 |
8 Dec 2026 |
Poynting's theorem and energy conservation. Force and momentum in electrodynamics. The Maxwell stress tensor. Use of the stress tensor to calculate forces. Homework #13 assigned.
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Reread Lecture 1; 361-372
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28 |
10 Dec 2026 |
Ohm's Law revisited. Magnetic flux conservation in very-high-conductivity media; Alfven's theorem. Mass, momentum, and energy conservation in magnetohydrodynamics.
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Reread 298-304, 372-376
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20 Dec 2026
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Final examination, 7:15-10:15 PM. |
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