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Date |
Topics |
Reading |
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1 |
26 Aug 2025 |
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 |
28 Aug 2025 |
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 |
2 Sept 2025 |
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 |
4 Sept 2025 |
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 |
9 Sept 2025 |
Gauss's Law. Example E calculations comparing the Gauss and Coulomb laws. Homework #3 assigned. |
69-76
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6 |
11 Sept 2025 |
Curl of E (= 0) in electrostatics. Electric (scalar) potential V, E = - grad V , etcCurl of E (= 0) in electrostatics. Electric (scalar) potential V, E = - grad V , etc. Arbitrariness of reference potential. Superposition. Example calculations of potential. Work and energy; relation to F and V; nonsuperposition. . Arbitrariness of reference potential. Superposition. Poisson's and Laplace's equation. Example calculations of potential. |
76-81, 88-94
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|
7 |
16 Sept 2025 |
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 |
18 Sept 2025 |
The Lemma: averages, lack of local extrema. Uniqueness of solutions to Poisson and Laplace equations. |
118-123
|
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9 |
23 Sept 2025 |
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
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|
10 |
25 Sept 2025 |
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 |
30 Sept 2025 |
Separation-of-variables problems with mixed and complicated boundary conditions; examples. Homework #6 assigned.
|
Reread 113-147
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12 |
2 Oct 2025 |
Calculation of V by method of images. Induced charge on conductors; example of point charge and conducting sphere.
|
124-129
|
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13 |
7 Oct 2025 |
Potential and field from an electric dipole. Solution of Laplace's equation by multipole expansions of the potential. Homework #7 assigned.
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147-156
|
| 14 |
9 Oct 2025 |
Summary of analytical, electrostatic E calculation paths; Purcell's Triangle. Return to the Lemma: the relaxation (finite-element) method for numerical solution of the Laplace equation. |
Reread 85-88; 115-116, 164-165
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16 Oct 2025 |
Midterm examination, covering all material introduced so far
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|
15 |
21 Oct 2025 |
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. Homework #8 assigned.
|
166-186
|
|
16 |
23 Oct 2025 |
Dielectrics and electric susceptibility. Some calculations of E and V for linear dielectrics. Forces and energy in dielectrics; capacitor oil-pump example. |
186-204
|
|
17 |
28 Oct 2025 |
Begin magnetostatics: Lorentz Force Law; cyclotron motion; force on a steady current. Current density, continuity equation. Calculation of magnetic field B from the Biot-Savart Law. Homework #9 assigned. |
209-229
|
|
18 |
30 Oct 2025 |
Divergence and curl of B. Derivation, and use, of Ampere's Law.
|
229-232
|
|
19 |
4 Nov 2025 |
Example calculations of B via Ampere's Law. The magnetic vector potential A; obtaining B by calculation of A first. Homework #10 assigned. |
232-238
|
|
20 |
6 Nov 2025 |
Boundary conditions in magnetostatics. Summary of calculation paths in magnetostatics, and conparison to electrostatics. Purcell's Other Triangle.
|
238-251
|
|
21 |
11 Nov 2025 |
Magnetic multipoles; calculation of magnetic dipole moment from current loop; torque on the loop; comparison between electric and magnetic dipoles. Magnetization vector field M and bound currents; auxiliary magnetic vector field H. Homework #11 asigned. |
251-255, 268-286
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|
22 |
13 Nov 2025 |
Calculation of B and H in linear media. Magnetic susceptibility and permeability, Ferromagnetism. |
286-294
|
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23 |
18 Nov 2025 |
Begin electrodynamics. Ohm's Law and its microscopic basis. Conductivity. EMF and magnetic force. Homework #12 assigned.
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299-315
|
|
24 |
20 Nov 2025 |
Induction and Faraday's Law. Magnetoquasistatics. Examples of use of Faraday's Law in field calculations.
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316-325
|
|
25 |
25 Nov 2025 |
Mutual and self inductance. Energy in magnetic fields. Homework #13 assigned.
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325-335
|
|
26 |
2 Dec 2025 |
Displacement current, and the finishing touches to the Maxwell equations.
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335-347
|
|
27 |
4 Dec 2025 |
Mass, momentum, energy, and magnetic flux conservation in plasmas: elements of magnetohydrodynamics.
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362-376
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14 Dec 2024
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Final examination, 7:15-10:15 PM EST |
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