*Syllabus*

Classical Electromagnetism

Physics 400A

Fall 2010

Instructor: Dr. Matt Anderson

Office: P140

Office Hours: Monday 1-2, Thursday 1-2

(I am also available for appointments by e-mail.)

E-mail: matt@sciences.sdsu.edu

TA: Melinda
Toth, mtoth06@cox.net

Office
hours: MWF 11-12, P146A

Class times: Tuesday & Thursday 11:00 AM – 12:15 PM, room P149

Textbook: *Introduction
to Electrodynamics, 3 ^{rd} ed.,* by
David J. Griffiths

Topics: Chapters 1-6 of Griffiths:

Vector Analysis

Electrostatics

Special Techniques

Electric Fields in Matter

Magnetostatics

Magnetic Fields in Matter

Grading: Homework: 20% (chapter homework will be due ~ every two weeks)

Midterms: 40% (Three midterms, drop the lowest one)

Final exam: 40% (Tuesday, Dec. 14, 10:30 –12:30)

In-class demos: Like charges repel, pith balls

Opposite charges attract, rolling soda can

Magnets deflect current

Learning Goals:

See attached document

*Learning Goals**

Classical Electromagnetism

Physics 400A

Fall 2010

Dr. Matt Anderson

** **

** **

** **

1. Math/physics
connection: Students should be able to translate a physical description
of a junior-level electromagnetism problem to a mathematical equation necessary
to solve it. Students should be able to explain the physical meaning of the
formal and/or mathematical formulation of and/or solution to a junior-level
electromagnetism problem. Students should be able to achieve physical insight
through the mathematics of a problem. Shall
we add something here about applications of E&M and/or experiments?

2. Visualize
the problem: Students should be able to sketch the physical parameters
of a problem (e.g., E or B field, distribution of charges, polarization), as
appropriate for a particular problem. What
type of problem can we give that is too hard without their 3310 knowledge?

3. Organized knowledge: Students should be
able to articulate the big ideas from each chapter, section, and/or lecture,
thus indicating that they have organized their content knowledge. They should
be able to filter this knowledge to access the information that they need to
apply to a particular physical problem, and make connections/links between
different concepts.

4. Communication. Students should be able
to justify and explain their thinking and/or approach to a problem or physical
situation, in either written or oral form.

5. Problem-solving techniques: Students
should be able to choose and apply the problem-solving technique that is
appropriate to a particular problem. This indicates that they have learned the
essential features of different problem-solving techniques (eg., separation of
variables, method of images, direct integration). They should be able to apply
these problem-solving approaches to novel contexts (i.e., to solve problems
which do not map directly to those in the book), indicating

9that they understand the essential features of the
technique rather than just the mechanics of its application. They should be
able to justify their approach for solving a particular problem.

...5a. Approximations:** **Students should be able to recognize when approximations are useful,
and use them effectively (eg., when the observer is very far away from or very
close to the source). Students should be able to indicate how many terms of a
series solution must be retained to obtain a solution of a given order.

...5b. Symmetries:** **Students should be able to recognize symmetries and be able to take
advantage of them in order to choose the appropriate method for solving a
problem (eg., when to use GaussÕ Law, when to use separation of variables in a
particular coordinate system).

...5c. Integration:** **Given a physical situation, students should be able to write down the
required partial differential equation, or line, surface or volume integral,
and correctly calculate the answer.

...5d. Superposition: Students should recognize that
– in a linear system – the solutions may be formed by superposition
of components.

6. Problem-solving
strategy: Students should be able to draw upon an organized set of
content knowledge (LG#3), and apply problem-solving techniques (LG#4) to that
knowledge in order to organize and carry out long analyses of physical
problems. They should be able to connect the pieces of a problem to reach the final
solution. They should recognize that wrong turns are valuable in learning the
material, be able to recover from their mistakes, and persist in working to the
solution even though they donÕt necessarily see the path to the solution when
they begin the problem. Students should be able to articulate what it is that
needs to be solved in a particular problem and know when they have solved it.

7. Expecting and checking solution: When
appropriate for a given problem, students should be able to articulate their
expectations for the solution to a problem, such as direction of the field,
dependence on coordinate variables, and behavior at large distances. For all
problems, students should be able to justify the reasonableness of a solution
they have reached, by methods such as checking the symmetry of the solution,
looking at limits, relating to cases with known solutions, checking units,
dimensional analysis, and/or checking the scale/order of magnitude of the
answer.

8. Intellectual maturity: Students should
accept responsibility for their own learning. They should be aware of what they
do and donÕt understand about physical phenomena and classes of problem. This
is evidenced by asking sophisticated, specific questions; being able to
articulate where in a problem they experienced difficulty; and take action to
move beyond that difficulty.

9. **MaxwellÕs
Equations. **Students should see the various laws in the course
as part of the coherent theory of electromagnetism; ie., MaxwellÕs equations.

10. Build on Earlier Material. Students
should deepen their understanding of Phys 196 material. I.e., the course should
build on earlier material.

__Overall Course Objectives:
Calculation and Computation__

Students will be able to:

Compute gradient, divergence, curl, and Laplacian

Evaluate line, surface, and volume integrals

Apply the fundamental theorem
for divergences (GaussÕ Theorem) in specific situations

Apply the fundamental theorem
for curls (StokeÕs Theorem) in specific situations

Apply CoulombÕs Law and
superposition principle to calculate electric field due to a continuous charge
distribution (uniformly charged line segment, circular or square loop, sphere,
etc.)

Apply GaussÕ Law to compute
electric field due to symmetric charge distribution

Calculate electric field from
electric potential and vice versa

Compute the potential of a
localized charge distribution

Determine the surface charge
distribution on a conductor in equilibrium

Use method of images to
determine the potential in a region Solve LaplaceÕs equation to determine the
potential in a region given the potential or charge distribution at the
boundary (Cartesian, spherical and cylindrical coordinates)

Use multipole expansion to
determine the leading contribution to the potential at large distances from a
charge distribution

Calculate the field of a
polarized object

Find the location and amount of
all bound charges in a dielectric material

Apply Biot-Savart Law and
AmpereÕs Law to compute magnetic field due to a current distribution

Compute vector potential of a
localized current distribution using multipole expansion

Calculate magnetic field from
the vector potential

Calculate the field of a
magnetized object

Compute the bound surface and
volume currents in a magnetized object

Compute magnetization, H field,
susceptibility and permeability

__Chapter Scale Learning Goals__

__ __

__ __

CHAPTER 1: Vector analysis

__TOPICS__

Div, grad, curl

Line, surface, volume integrals

Curvilinear coordinates

Dirac delta function

Vector fields (potentials)

__PREREQUISITES: Students should already be able to... __

1. Be
able to compute correctly div, grad and curl in rectangular coordinates for any
test function

2. Do
a path integral along a specific path—eg. Griffiths 2.20

3. Be
able to expand 1/1+e and 1/1-e when e is very small (Taylor series).

__Students should be able to: __

1. Evaluate
the integral from negative infinity to infinity of the delta function, d(x)

2. Evaluate
the 3-dimensional divergence of 1/r2 in the r-hat direction [4 d3¨]

3. Evaluate
the integral of a function times the delta function

4. Be
able to evaluate the integral of 1/(x-r)3/2dx

5. Give
a geometrical description of the divergence theorem, and fundamental theorem
for curls.

6. Change a multidimensional integral in
Cartesian coordinates to one in another coordinate system using the Jacobian.

CHAPTER 2: Electrostatics

__TOPICS__

Electric field, CoulombÕs law

GaussÕ Law, divergence and curl
of E

Potential

Poisson & Laplace equation

Work & energy

Conductors

__PREREQUISITES: Students should already be able to... __

1. State
GaussÕ Law and construct the 3 Gaussian surfaces (sphere, cylinder, pillbox).

2. Use
Cartesian, spherical and cylindrical coordinates appropriately when
constructing integrals and surface and volume elements.

__Electric Field__

1. Students
should be able to state CoulombÕs Law and use it to solve for E above a line of
charge, a loop of charge, and a circular disk of charge.

2. Students
should be able to solve surface and line integrals in curvilinear coordinates
(when given the appropriate formulas, as in the inner-front cover of
Griffiths).

__Divergence and Curl of E; GaussÕ Law__

1. Students
should recognize when GaussÕ Law is the appropriate way to solve a problem (by
recognizing cases of symmetry; and by recognizing limiting cases, such as being
very close to a charged body).

2. Students
should be able to recognize that E comes out of the Gaussian integral only if
it is constant along the Gaussian surface.

3. Students
should be able to recognize GaussÕ Law in differential form and use it to solve
for the charge density given an electric field E.

__Electric Potential__

1. Students
should be able to state two ways of calculating the potential (via the charge
distribution and via the E-field); indicate which is the appropriate
formulation in different situations; and correctly evaluate it via the chosen formulation.

2. Students
should be able to calculate the electric field of a charge configuration or
region of space when given its potential.

3. Students
should be able to state that potential is force per unit charge, and give a
conceptual description of V and its relationship to energy.

4. Students
should be able to explain why we can define a vector potential V (because the
curl of E is zero and E is a conservative field).

5. Students
should be able to defend the choice of a suitable reference point for
evaluating V (generally infinity or zero), and explain why we have the
freedom to choose this reference point (because V is arbitrary with respect to
a scalar – its slope is important, not its absolute value).

__Work & Energy__

Students should be able to
calculate the energy stored in a continuous charge distribution when given the
appropriate formula Students should be able to explain in words what this
energy represents.

__Conductors__

Students should be able to
sketch the induced charge distribution on a conductor placed in an electric
field. Students should be able to
explain what happens to a conductor when it is placed in an electric field, and
sketch the E field inside and outside a conducting sphere placed in an electric
field. Students should be able to explain how conductors shield electric
fields, and describe the consequences of this fact in particular physical
problems (e.g., conductors with cavities). Students should be able to state that
conductors are equipotentials, that E=0 inside a conductor, that E is
perpendicular to the surface of a conductor (just outside the conductor), and
that all charge resides on the surface of a conductor.

__MaxwellÕs Equations__

Students should be able to interpret
the first and second MaxwellÕs equations for electrostatics ( and ) and use them to describe electrostatics (i.e., GaussÕ Law
is just one application of the first law).

CHAPTER 3: Special Techniques

__TOPICS__:

1. LaplaceÕs
equation

2. Boundary
conditions and uniqueness

3. Method
of images

4. Separation
of variables in Cartesian and spherical

5. Multipole
expansion

__PREREQUISITES: Students should already be able
to...__

1. Recognize the wave equation in
Cartesian coordinates, and state that eikx is
a solution

2. Recognize the solution to
separation of variables in Cartesian coordinates.

3. Recognize that a function can be
expanded in terms of a complete basis, such as sin and cos.

4. State that conductors are
equipotentials.

__LaplaceÕs equation__

1. Students
should recognize that the solution to LaplaceÕs equation is unique.

__Method of Images__.

1. Students
should realize when the method of images is applicable and be able to solve
simple cases.

2. Students should be able to explain the
difference between the physical situation (surface charges) and the
mathematical setup (image charges).

__Separation of variables/boundary value problems__

1. Students
should be able to state the appropriate boundary conditions on V in
electrostatics and be able to derive them from MaxwellÕs equations.

2. Students
should recognize where separation of variables is applicable and what
coordinate system is appropriate to separate in.

3. Students
should be able to outline the general steps necessary for solving a problem
using separation of variables.

4. Students
should be able to state what the basis sets are for separation of variables in
Cartesian and spherical coordinates (i.e., exponentials, sin/cos, and Legendre
polynomials.)

5. Students
should be able to apply the physics and symmetry of a problem to state
appropriate boundary conditions.

6. Students
should be able to solve for the coefficients in the series solution for V, by
expanding the potential or charge distribution in terms of special
functions and using the completeness/orthogonality of the special functions,
and express the final answer as a sum over these coefficients.

__Multipole expansions__

1. Students
should be able to explain when and why approximate potentials are useful.

2. Students
should be able to identify and calculate the lowest-order term in the monopole
expansion (i.e., the first non-zero term).

3. Students should be able to sketch the
direction and calculate the dipole moment of a given charge distribution.

CHAPTER 4: Electric
Fields in Matter

__TOPICS__

Polarization & dielectrics
Field of polarized object (bound charges, field inside dielectric)

Electric displacement

Linear dielectrics:
Susceptibility, permittivity, dielectric constant

Boundary value problems with
dielectrics

__Polarization and dielectrics__

1. Students
should be able to go between two representations of dipoles – as point
charges, and as generalized dipole vectors – for simple charge
configurations.

2. Students
should be able to calculate the dipole moment of a simple charge distribution.

3. Students
should be able to name 4 similarities and differences between a conductor and a
dielectric (both shield E, conductor shields E completely, dielectric
shields via fixed dipoles, conductor shields via mobile electrons).

4. Students
should be able to predict whether a particular pattern of polarization will
result in bound surface and/or volume charge

5. Students
should be able to explain the physical origin of bound charge.

__Field of a polarized object__

1. Students
should be able to sketch the E field inside and outside a dielectric sphere
placed in an electric field.

2. Students
should be able to explain what happens to a dielectric, when it is placed in an
electric field.

3. Students
should be able to explain the difference between free and bound charge.

4. Students should be able to identify
the appropriate boundary conditions on D given its relationship to E and Qf.

__ __

__Electric displacement__

1. Students
should be able to sketch the direction of D, P, and E for simple problems
involving dielectrics

2. Students
should be able to calculate the E field inside a dielectric when given epsilon
and the free charge on the dielectric.

3. What else do we want students to know
about D?

__Linear dielectrics__

1. Students should be able to
articulate the difference between a linear and nonlinear dielectric.

2. Students should be able to write
down MaxwellÕs equations (for electrostatics) in matter, when given the
appropriate equations in vacuum.

3. Students
should be able to identify the appropriate boundary conditions on D, given its
relationship to E.

CHAPTER 5:
Magnetostatics

__TOPICS__

Currents and charge density

Magnetic fields and forces
(Lorentz force law)

Biot-Savart law

Divergence and curl of B
(AmpereÕs Law)

Magnetic vector potential

__PREREQUISITES: Students should already be able to...__

1. Write
down Lorentz force law

2. Know
the right-hand rule and how to apply it

__Currents and charge density__

1. Students
should be able to calculate current density J given the current I, and know the
units for each.

2. Students
should be able to explain, in words, what the charge continuity equation means.

3. Students
should be able to state the vector form of OhmÕs Law ( )
and when it applies.

4. Students should be able to calculate
the current I, K and J in terms of the velocity of the particle or in terms of
each other.

__Magnetic fields and forces__

1. Students
should be able to describe the trajectory of a charged particle in a given
magnetic field.

2. Students
should be able to sketch the B field around a current distribution, and explain
why any components of the field are zero.

3. Students should be able to explain why
the magnetic field does no work using concepts and mathematics from 342.

__Biot-Savart Law__

1. Students
should be able to state when the Biot-Savart Law applies (magnetostatics;
steady currents, dp/dt=0).

2. Students
should be able to compare similarities and differences between the Biot-Savart
law and CoulombÕs Law.

3. Students should be able to choose when
to use Biot-Savart Law versus AmpereÕs Law to calculate B fields, and to
complete the calculation in simple cases.

__ __

__Divergence and curl of B (AmpereÕs Law)__

1. Students
should be able to draw appropriate Amperian loops for the cases in which
symmetry allows for solution of the B field using AmpereÕs Law (ie., infinite
wire, infinite plane, infinite solenoid, toroids), and calculate Ienc.

2. Students
should be able to make comparisons between E and B in MaxwellÕs equations (what
exactly do we want?)

__Magnetic vector potential__

1. Students should be able to explain
why the potential A is a vector for magnetostatics, whereas itÕs a scalar (V)
in electrostatics. Ie., that the source of magnetic fields (the current) is a
vector, whereas the source of electric fields (charge) is not.

2. Students
should recognize that A does not have a physical interpretation similar to V,
but be able to identify when it is useful for solving problems. *How to
phrase this so that it doesnÕt sound like ÒAÓ is just useless mathematics?*

__Separation of
variables/boundary value problems__

1. Students should be able to state
the appropriate boundary conditions on B in magnetostatics and be able to
derive them from MaxwellÕs equations

__MaxwellÕs Equations__

1. Students should be able to interpret the third
and fourth MaxwellÕs equations for electrostatics ( and ) and
use them to describe magnetostatics (i.e., AmpereÕs Law and Biot-Savart law are
just applications of these laws).

CHAPTER 6: Magnetic Fields in Matter

__TOPICS__

1. Magnetization
– diamagnets, paramagnets, ferromagnets

1. Field of
magnetized object (bound currents)

2. Auxiliary
field H

3. Linear
and nonlinear media: susceptibility, permeability

__PREREQUISITES: Students should already be able to...__

__Magnetization__

1. Students
should be able to calculate the torque on a magnetic dipole in a magnetic
field.

2. Students
should be able to explain the difference between para, dia, and ferromagnets,
and predict how they will behave in a magnetic field.

__The Field of a magnetized object__

1. Students
should be able to predict whether a particular magnetization will result in a
bound surface and/or volume current, for simple magnetizations.

2. Students
should be able to give a physical interpretation of bound surface and volume
current, using StokesÕ Theorem.

__Auxiliary field H__

1. Students
should be able to calculate H when given B or M

2. Students
should recognize that H is a mathematical construction, whereas B and M are
physical quantities.

3. Students
should be able to use H to calculate B when given Jf for an appropriately
symmetric current distribution.

4. Students
should be able to articulate in which physical situations it is useful to use
H.

5. Students should be able to identify the appropriate
boundary conditions on H given its relationship to M and Kf.

***Note: Help me identify typos and/or necessary
additions.**

**This text is adapted from the following website:**

**http://www.cwsei.ubc.ca/resources/files/Learning_Goals_at_UBC_and_CU_examples.pdf**