Phys 302/Elec 206: Electromagnetism
Fall 2020
Topics Covered in Lectures
|
Lecture Number |
Date |
Content |
Corresponding Reading material* |
|
1 |
Oct. 05 |
Vector algebra, dot product, norm, unit
vectors, orthogonal vectors, cross product, Kronecker delta, Levi Civita
symbol, expressing the cross product in terms of the Levi Civita symbol. |
Pages 1-6 of the textbook
(Griffiths’ 4th Edition) |
|
2 |
Oct. 07 |
Consequences
of expressing the cross product in terms of the Levi Civita symbol: Various
properties of the cross product, the dot product of a vector with the cross
product of two other vectors, expressing the determinant of a matrix in terms
of the Levi Civita symbol. Statement and proof of a basic identity for the
product of a pair of Levi Civita symbols with a common label summed over. |
Page 6 of the textbook |
|
3 |
Oct. 09 |
Identities
involving the cross product and dot product of more than two vectors and
their derivation using the properties of the Levi Civita symbol;
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-values functions of
several real variables: Divergence and Laplacian |
Pages 6-8 & 13-18 of the
textbook |
|
4 |
Oct. 12 |
Curl
and some of its properties, Integration in 1, 2, and 3 dimensions, line
integral, surface integral, volume element in Cartesian, cylindrical, and
spherical coordinates |
Pages 18-28 of the textbook |
|
5 |
Oct. 14 |
Flux of
a vector field through a surface, Fundamental Theorem of Calculus, Stokes’
Theorem, Divergence Theorem; basic motivation for introducing Dirac delta
function |
Pages 28-38 of the textbook |
|
6 |
Oct. 16 |
Test
function, Non-convergent sequences of functions defining a linear
transformation on the space of test functions, generalized functions of
distributions, equal generalized functions, the step function and its
derivative |
Pages 46-48 of the textbook |
|
7 |
Oct. 19 |
Derivative
of the Heaviside step function is the Dirac delta function, Some basic
properties of the Dirac delta function, delta function in 2 and 3 dimensions,
divergence of r/|r|3 for nonzero r. |
Pages 48-51 of the textbook |
|
8 |
Oct. 21 |
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 |
|
9 |
Oct. 23 |
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 |
Pages 63-64, 71 of the textbook |
|
Quiz 1 |
Oct. 24 |
|
|
|
10 |
Oct. 26 |
Gauss’s
law, flux lines (lines of electric force), electric field of a uniformly
charged infinite plane, electric field of a parallel pair of uniformly
charged infinite planes, the electric potential and the work done by the
electric force of a continuous charge distribution |
Pages 64-79 of the
textbook |
|
11 |
Oct. 30 |
Electric potential as a line integral of the
electric field, the potential for a uniformly shared spherical shell and its
thin-shell limit |
Pages 79-83 of the textbook |
|
12 |
Nov. 02 |
Poisson and Laplace’s equations, boundary conditions
on the electric field along the interface of two regions in space |
Pages 83-91 of the textbook |
|
13 |
Nov. 04 |
The energy and energy density of the electric field |
Pages 91-97 of the textbook |
|
14 |
Nov. 06 |
Insulators and conductors, electrostatic properties
of a conductor, electrostatic pressure on a conductor |
Pages 97-105 of the textbook |
|
Quiz 2 |
Nov. 07 |
|
|
|
15 |
Nov. 09 |
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; Uniqueness theorem
for the solutions of the Poisson’s equation |
Pages 113-121 of the textbook |
|
16 |
Nov. 11 |
Uniqueness theorem for the solutions of the
Poisson’s equation in a region surrounded by conductors that can be charged,
capacitors |
Pages 121-124
& 105-107 of
the textbook |
|
17 |
Nov. 13 |
The method of images |
Pages 124-130 of the textbook |
|
18 |
Nov. 16 |
Solution of the Laplace’s equation using the method
of separation of variables in Cartesian coordinates for an effectively
two-dimensional electrostatics problem |
Pages 130-135 of the textbook |
|
19 |
Nov. 18 |
Solution of the Laplace’s equation using the method
of separation of variables in Cartesian coordinates in three dimensions |
Pages 135-141 of the textbook |
|
20 |
Nov. 20 |
Solution of the Laplace’s equation using the method
of separation of variables in spherical coordinates |
Pages 141-150 of the textbook |
|
Quiz 3 |
Nov. 21 |
|
|
|
21 |
Nov. 23 |
Potential for an electric dipole, dipole moment,
multipole expansion of the potential for a localized continuous distribution
of charges, the electric field of a dipole |
Pages 150-160 of the textbook |
|
22 |
Nov. 25 |
The force and torque exerted by an external electric
field on a dipole, polarization of a molecule, the electric potential for a
polarized dielectric medium, the surface and volume bound charges and their
densities |
Pages 167-179 of the textbook |
|
23 |
Nov. 27 |
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, boundary
conditions on the interface of two adjacent homogeneous isotropic linear
dielectric media |
Pages 179-192 of the textbook |
|
24 |
Nov. 30 |
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 192-194 of the textbook |
|
25 |
Dec. 02 |
Energy of a dielectric medium, electric force
exerted on a dielectric |
Pages 197-205 of the textbook |
|
26 |
Dec. 04 |
Magnetostatics: Lorentz force, work done by a
magnetic force, electric currents, magnetic force on a wire carrying a
current |
Pages 212-219 of the textbook |
|
Quiz 4 |
Dec. 05 |
|
|
|
27 |
Dec. 07 |
Magnetic forces through a wire, surface and volume
current densities, local charge conservation and continuity equation |
Pages 221-226 of the textbook |
|
28 |
Dec. 09 |
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,
divergence and curl of magnetic field due to a current distribution, Ampere’s
law |
Pages 226-235 of the textbook |
|
29 |
Dec. 11 |
Integral form of Ampere’s law and some of its basic
applications, the field equations of electro/magnetostatics, the vector
potential and the proof of its existence |
Pages 236-245 of the textbook |
|
Winter
Break |
|
|
|
|
30 |
Dec. 21 |
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 and current loops obtained
by joining line segments, multipole expansion of the vector potential and
lack of magnetic monopole terms |
Pages 246-251
& 254-255 of
the textbook |
|
31 |
Dec. 23 |
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 loop into smaller current loop |
Pages 255-258 of the textbook |
|
32 |
Dec. 25 |
Force and torque exerted on a rectangular current
loop by a constant external magnetic field, magnetization of dielectric
media, volume and surface bound currents and their densities, magnetic
induction (H) field and the field equations of electro-magnetostatics in a
dielectric medium |
Pages 269-286 of the textbook |
|
Quiz 5 |
Dec.26 |
|
|
|
33 |
Dec. 28 |
Boundary conditions on the magnetic field, vector
potential, and magnetic induction fields on the interfaces separating two
media |
Pages 251-253
& 287of the
textbook |
|
34 |
Jan. 4 |
Magnetic field in linear media, susceptibility and
permeability tensors, isotropic magnetic material and scalar susceptibility and
permeability, classification of isotropic linear magnetic material, Ohm’s law |
Pages 287-307 of the textbook |
|
Quiz 6 |
Jan. 04 |
|
|
|
35 |
Jan. 06 |
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 307-316 & 336-342 of the textbook |
|
36 |
Jan. 08 |
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 316-331 of the textbook |
Note: *The pages from the textbook listed above may not include some of the
material covered in the lectures.