Course outline: The outline can be downloaded here.
Class timings: 4:30 to 5:45 pm, Tuesday and Thursday, Room: 202 SSE Complex.
Mathematical Preliminaries (4 lectures):
- Differential vector calculus, Levi-Civita symbol
- Vector integral theorems
- Dirac delta function
- Fourier theory
- Helmholtz’s theorem
- HW1: Mathematical preliminaries (due date: Monday, 19 September, 12 pm). Solution can be seen here.
Review of Maxwell’s Equations (2.5 lectures):
- Continuity equation
- Biot-Savart law, Oersted’s law, Coulomb’s law, forces between current carrying conductors, etc.
- Necessity of displacement current
- Matching conditions
- Maxwell’s equations in free space and inside matter
- HW2: Maxwell’s Equations: a unified view (due date: Wednesday, 28 September, 12 pm).
Electrostatics (4 lectures):
- Coulomb’s law from Maxwell’s equations
- Forces on torques on charge distributions
- Electrostatic potentials, self energy and interaction energies
- Reciprocity theorem
- Maxwell’s stress tensor
- Plotting electric field lines
- HW3: Homework 3 (due date: Monday, 17 October, 12 pm). Article on drawing field lines using Gauss’s law to accompany Q. 3. Solution posted here.
Electric Multipoles (4 lectures):
- Multipole expansion
- Electric dipole, point dipole and their potential, electric field
- Force, torque and energy of an electric dipole
- Electric quadrupoles
- HW4: Homework 4. (due date: Friday, 23 October, 5 pm). Solution can be seen here. Errors and omissions are expected.
Conductors (4 lectures)
- Spherical multipole expansion, spherical conductor inside a uniform electric field. Some example calculations.
- Capacitance matrix
- Energy of a system of charged metals as a function of the capacitance matrix
- Energy and forces on conductors
- HW5: I like you to solve the three suggested problems in the Appendix of Electric fields in the presence of conducting objects by J.L.R. Marrero, AJP 78, 639 (2010). Solving this first requires you to actively read the uploaded article. (due date:Tuesday, 15 November, 12 pm).
Dielectrics and Polarization (3 lectures)
- Polarization field, polarization charges
- Uniformly polarized materials
- Potential and field due to combinations of free and polarized charges
- Energy inside a dielectric
- Forces on dielectrics
- Boundary conditions for the auxiliary field D
- HW6: Homework 6. (due date: Tuesday, 29 November, 12 pm). Solution.
Electric Currents (3 lectures)
- Steady currents and continuity equation
- Matching conditions for currents
- Resistance and relationship between resistance and capacitance
- EMF and diffusion current (do-it-yourself)
- Currents inside vacuum and Child-Langmuir equation
- Joule heating
- HW7: Homework 7 (due date: Tuesday, 13 December, 12 pm). Solution is here.
Magnetostatics (3 lectures)
- Biot-Savart law
- Magnetic scalar and vector potential
- Ampere’s law