Date | Notes |
M 8/24 | Classes Begin: Introduction, Administrivia. Begin Chapter 1, Coulomb's Law. Electric field of long wire. |
W 8/26 | Divergence of electric field. ∇⋅(x/r^{3}); digression on δ-functions. Gauss's Law ∇⋅E = ρ/ε_{0} ; ∇×E = 0 |
F 8/28 | More properties of δ-functions. |
M 8/31 | Potential E = −∇Φ, Poisson's equation ∇^{2}Φ = −ρ/ε_{0}. Potential of long wire, renormalization. Boundary conditions. |
W 9/2 | Electrostatic energy, ideal conductors, capacitance. |
F 9/4 | Greens identities, Green's theorem, uniqueness, Green's functions (Dirichlet, Neumann) |
M 9/7 | Labor Day (no class) |
W 9/9 | Begin Chapter 2: Images in a plane, images in a sphere. Green's function for a sphere. Two hemispheres held at opposite potential |
F 9/11 | Potential at center of a sphere. Two hemispheres held at opposite potential, exact solution on-axis, approximate solution. |
M 9/14 | Images in two parallel planes. Separation of variables in Cartesian coordinates. |
W 9/16 | Cube with one face at V_{0}. Summing a series. |
F 9/18 | Fourier sine series for δ(x−x'). Green's function for a square. |
M 9/21 | Finish Green's function for a square. Begin Chapter 3: Separation of variables in spherical coordinates, radial solution. |
W 9/23 | Spherical coordinates. Legendre's equation. Rodrigues' formula preliminaries. |
F 9/25 | Rodrigues' formula. Orthogonality, Beta functions and integral normalization of Legendre polynomials. |
M 9/28 | P_{l}(0). Legendre polynomial expansion of step function. Sphere with two hemispheres at opposite potential. |
W 9/30 | Expansion of Green's function in Legendre polynomials. m ≠ 0, Legendre functions P_{l}^{m}. Spherical harmonics. |
F 10/2 | Addition theorem for spherical harmonics. Begin Green's function for V between two spheres. |
M 10/5 | Green's function between two spheres. Limits. Conducting sphere in a uniform applied field. |
W 10/7 | Laplace's equation in cylindrical geometry. Bessel's equation. |
F 10/9 | Bessel functions, recursions, zero[e]s, orthogonality. |
M 10/12 | Bessel function integral normalization. Bessel function expansion of step function. |
W 10/14 | Continuous k. More about Bessel function. |
Thursday 10/15 | Midterm Exam 7:30pm NEB 202 |
F 10/16 | Finishing Bessel functions. |
M 10/19 | Begin Chapter 4, Multipole expansion of potential, electrostatic energy. |
W 10/21 | Spherical average ⟨ E ⟩_{R}. Electrostatics with polarization. |
F 10/23 | Linear dielectrics, susceptibility, relative permittivity. Models of polarizability. Dielectric sphere in uniform applied field. |
M 10/26 | Plane interface between two media, images revisited. Stored energy with dielectrics. |
W 10/28 | Begin Chapter 5, Magnetostatics. Biot-Savart Law. Force between currents. |
F 10/30 | Ampère's Law, no magnetic monopoles. Vector potential, straight wire, begin current loop. notes now up! |
M 11/2 | Vector potential of current loop, Elliptic integrals. |
W 11/4 | Far and near limits of current loop. Magnetic multipole expansion, magnetic dipole moment, dipole field. |
F 11/6 | Homecoming (no class) |
M 11/9 | Force on a dipole. Torque on a dipole. Magnetic moment and angular momentum. ⟨ B ⟩_{R}, Magnetization. |
W 11/11 | Veteran's Day (no class) |
F 11/13 | Idealizations: linear permeability, hard magnetization. Permeable sphere in uniform applied field. |
M 11/16 | Bar magnet as surface current, as surface charge. Begin induction, Faraday's law. |
W 11/18 | Conductivity, magnetic diffusion, skin depth. |
F 11/20 | Energy in magnetic field. Inductance. Displacement current. |
M 11/23 | Begin Chapter 6, Maxwell's equations. Gauge transformation. Wave equation, separation of variables. Green's function in Fourier space. |
W 11/25 F 11/27 |
Thanksgiving (no class) |
M 11/30 | Advanced and retarded Green's functions for wave equation. Poynting's Theorem. |
W 12/2 | Field momentum density, momentum flux,
Maxwell stress tensor.
Angular momentum of static electric and magnetic monopole fields. |
F 12/4 | Harmonic time dependences. Poynting revisited, impedance, resistance, reactance. Rotations, orthogonal transformations, generators. |
M 12/7 | Tensors. Vector content of Maxwell's equations. |
W 12/9 | Duality rotation. Last day of class. |
Th 12/17 | Final Exam, 5:30–7:30pm (Exam Period 17E) |