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’ 4th
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.