Phys 302/Elec 206: Electromagnetism

Fall 2021

Topics Covered in Lectures

Lecture Number	Date	Content	Corresponding Reading material*
1	Sep. 27	Vector algebra, dot product, norm, unit vectors, orthogonal vectors, cross product and its basic properties, the dot product of a vector with the cross product of two other vectors, Kronecker delta symbol	Pages 1-7 of the textbook (Griffiths’ 4^th Edition)
2	Sep. 29	Levi Civita symbol and the cross product of space vectors, expressing the determinant of a 3 x 3 ,matrix in terms of the Levi Civita symbol, basic identity for the product of a pair of Levi Civita symbols with a common label summed over, derivation of identities involving the cross product and dot product of more than two vectors using the properties of the Levi Civita symbol	Page 6-8 of the textbook
3	Oct. 04	Vector-valued functions of a single real variable: Limit, derivative, and integration, scalar functions of several real variables: Limit, directional and partial derivatives, gradient, differential, Vector-valued functions of several real variables: Divergence, Laplacian, and curl	Pages 13-22 of the textbook
4	Oct. 06	Curl and some of its properties, Integration in 1, 2, and 3 dimensions, line integral, surface integral, Flux of a vector field through a surface, volume element in Cartesian, cylindrical, and spherical coordinates, Fundamental Theorem of Calculus	Pages 22-29 of the textbook
5	Oct. 11	Stokes and Divergence Theorems; basic motivation for introducing Dirac delta function, test functions and non-convergent sequences of functions defining a linear transformation on the space of test functions, generalized functions	Pages 29-38 & 46-47 of the textbook
6	Oct. 13	Review of notion of a generalized function, equal generalized functions, the Heaviside step function and its derivative, some basic properties of the Dirac delta function, delta function in 2 and 3 dimensions, divergence of r/|r|^3 for nonzero r.	Pages 46-50 of the textbook & pages 100-116 of Kusse & Westwig’s “Mathematical Physics.”
7	Oct. 18	Generalized functions of several variables and their equality, the proof that the divergence of r/|r|^3 is 4πδ^(3)(r). Some consequences of the Stokes’ and Divergence theorem: Characterization of the divergence-free and curl-free vector-valued functions (vector fields), scalar and vector potentials, decomposition of vector fields as the sum of the gradient of a scalar potential and the curl of a vector potential; Electrostatics: Coulomb’s law, electric fields of point charges, the linearity or superposition principle	Pages 50-54 & 59-63 of the textbook
8	Oct. 20	Electric field for a continuous charge distributions in 3 dimensions, electric field for a charged wire or surface of arbitrary shape, calculation of the electric field of a uniformly charged line segment, Gauss’s law, flux lines (lines of electric force)	Pages 63-68 & 71 of the textbook
Midterm Exam 1	Oct. 24
9	Oct. 25	Electric field of a uniformly charged infinite plane, electric field of a pair of parallel uniformly charged infinite planes, the electric potential and the work done by the electric force of a continuous charge distribution, electric potential as a line integral of the electric field, the electric field for a uniformly charged spherical shell	Pages 71-88 of the textbook
10	Oct. 27	Electric potential for a uniformly charged spherical shell, energy and energy density of the electric field	Pages 91-97 of the textbook
11	Nov. 01	Poisson and Laplace’s equations, boundary conditions on the electric field and electric potential along the interface of two regions in space, Insulators and conductors, electrostatic properties of a conductor	Pages 83-91 & 97-103 of the textbook
12	Nov. 03	Force exerted by an electric field on a conductor, electrostatic pressure on a conductor; Basic properties of the solutions of the Laplace’s equation in 1D, 2D, and 3D; the equality of the electric field at the center of a sphere to its average on the surface of the sphere	Pages 103-105 & 113-119 of the textbook
13	Nov. 08	Uniqueness theorem for the solutions of the Poisson’s equation, Electric field in a region surrounded by neutral or charged conductors, capacitors; Basic idea of the method of images	Pages 119-125 & 105-107 of the textbook
14	Nov. 10	Method of images, solution of the Laplace’s equation using the method of separation of variables in Cartesian coordinates for an effectively two-dimensional electrostatics problem (Part 1)	Pages 124-133 of the textbook
Winter Break
15	Nov.22	Solution of the Laplace’s equation using the method of separation of variables in Cartesian coordinates for an effectively two-dimensional electrostatics problem (Part 2), solution of the Laplace’s equation in three dimensions using separation of variables in spherical coordinates (Part 1)	Pages 130-141 of the textbook
16	Nov. 24	Solution of the Laplace’s equation in three dimensions using separation of variables in spherical coordinates (Part 2), potential for an electric dipole, dipole moment	Pages 141-151 of the textbook
17	Nov. 29	Multipole expansion of the potential for a localized continuous distribution of charges, electric field of a dipole, force and torque exerted by an external electric field on a dipole, polarization of a molecule	Pages 151-172 of the textbook
18	Dec. 01	Electric potential for a polarized dielectric medium, the surface and volume bound charges and their densities; Electrostatics in a dielectric medium: Displacement field, and the Gauss’s law in a dielectric, boundary conditions on the interface of two adjacent dielectric media, linear dielectric media, polarization tensor, isotropic linear media and their permittivity, homogeneous isotropic linear media and their dielectric constant	Pages 172-186 of the textbook
Midterm Exam 2	Dec. 04
19	|Dec. 06	Electric displacement, polarization field, and bound charge density for a homogeneous, isotropic, linear dielectric medium, boundary-value problem with dielectrics, calculation of the electric field and bound charge distribution in a homogeneous isotropic linear dielectric filling a ball of radius R placed in an electric field that is constant far from the ball	Pages 186-197 of the textbook
20	Dec. 08	Energy of a dielectric medium, energy stored in a dielectric parallel-plate capacitor, electric force exerted on a dielectric; Magnetostatics: Lorentz force	Pages 197-214 of the textbook
21	Dec. 13	Lorentz force law, motion of a point charge in constant electric and magnetic fields that are orthogonal, work done by a magnetic force, magnetic field as a tool for redirecting electric forces, current true a wire, magnetic force on a wire carrying a current	Pages 214-221 of the textbook
22	Dec. 15	Magnetic forces on wires, conducting surface, conducting three dimensional objects carrying currents or current densities, surface and volume current densities, charge conservation of the continuity equation, SI units for current and magnetic field, Biot-Savart’s law, calculation of the magnetic field along the symmetry axis of a circular current loop with constant current	Pages 222-230 of the textbook
23	Dec. 20	Divergence and curl of the magnetic field due to a continuous current distribution, Ampere’s law and its integral form, Magnetic field of an infinite straight wire carrying a constant current, magnetic field due to an infinite conducting plate having a constant surface current density, the field equations of electro/magnetostatics	Pages 233-244 of the textbook
24	Dec. 22	Vector potential, proof of its existence and non-uniqueness, gauge transformations of the vector potential, divergence-free vector potentials, vector potentials that solve a Poisson equation and their generic form, vector potential and magnetic fields of a straight line segment carrying a constant current	Pages 245-250 of the textbook
Midterm Exam 3	Dec. 26
25	Dec. 27	Vector potential due to a current loop made of straight line segments, multipole expansion of the vector potential, magnetic dipole moment and a proof of its appearance in the expression for the dipole terms in the multipole expansion of the vector potential, decomposition of current loops into smaller current loop, force and torque exerted on a rectangular current loop by a constant external magnetic field, magnetization of dielectric media	Pages 254-276 of the textbook
26	Dec. 29	Volume and surface bound currents and their densities, magnetic induction (H) field and the field equations of electro-magnetostatics in a dielectric medium, magnetic field in linear media, susceptibility and permeability tensors, isotropic magnetic material and scalar susceptibility and permeability, classification of isotropic linear magnetic material, boundary conditions on the magnetic field and vector potential on the interfaces separating two media	Pages 276-293 & 251-253 of the textbook
27	Jan. 03	Electrodynamics: Ohm’s law, Joule’s heating law, electromotive force, motional electromotive force, Faraday’s law, Maxwell’s resolution of the problem with Ampere’s law in electrodynamics and Maxwell’s equations in vacuum	Pages 300-324 of the textbook
28	Jan. 05	The electric field induced by a changing magnetic field that is confined to an infinite cylinder and is directed along the symmetry axis of the cylinder, the current induced in a circular loop encircling this cylinder, mutual and self-inductance, current in RL and RLC circuits	Pages 325-331 of the textbook

Note: *The pages from the textbook listed above may not include some of the material covered in the lectures.