1
1
2
2
3
3
attracted
repelled
?
The interaction between 2 and 3 is:
A) Attractive
B) Repulsive
Forces between charged spheres
What can we deduce about the amount of
charge on the two equal mass spheres:
A.Equal amount of charge on each sphere
B.The cha
1
Current
So far, we talked about electrostatics
When
applied to conductors charges move = current
General Physics II, 171.102
Net charge per unit time
through some crosssection A
= Flux of charge
Unit: Ampere
Lecture 13
2
Current density
Charge carriers
1
RC Circuits
switch
+
+ +

charging
+
+
discharging
General Physics II, 171.102
Circuit which contains both a
R and a C
Charges move from battery
onto plates of C
Potential energy is being
loaded into the capacitor
Flip the switch
Charges move from the
Atomic spectra
1
Immensely useful.
But why are there
lines? Why discrete?
General Physics II, 171.102
Lecture 36
The birth of Quantum Mechanics
Werner Heisenberg (1925, at age 24)
invents matrix mechanics
2
(with help of Born and Jordan)
first serious use
Ampere's Law
If no currents enclosed:
Contour can have an arbitrary shape
Could enclose multiple currents
Very powerful statement about property of B field
1
With symmetry, a good way to determine B
(Similar symmetries in play as for Gauss's Law)
General
Circuit rules
Ohm's Law:
For capacitors:
1
on any resistor
on any capacitor
Conservation of charge current into any junction is
conserved!
Junction rule, Kirchoff's 1st rule, etc.
sum of voltages around any loop is zero!
Loop rule, Kirchoff's 2nd rule, et
1
Limitation's of Ohm's Law
DrudeLorenz's model describes
conduction of a variety of materials
and under a variety of conditions (esp. room temperature)
dependence on temperature, etc. (e.g. `Hall effect')
Nevertheless, it's just a model
IV curves for f
1
BiotSavart Law
Sources of magnetic field:
permanent magnets need Quantum Physics to understand
currents
Experiments show how the B
field is oriented near conductors
General Physics II, 171.102
Lecture 19
2
BiotSavart Law
Experiment:
B field lines are
Atomic spectra
1
Immensely useful.
But why are there
lines? Why discrete?
General Physics II, 171.102
Lecture 38
2
Wave function
Matter particles (e.g. electron) are described by their wave
function:
it's a complex number
is a probability density to obser
1
Single photon doubleslit experiment
Taylor in 1909 repeated Young's double slit experiment,
but with one twist:
source was weak it was emitting one photon at a time
used photographic film as screen, and waited very very long
time
the interference
patt
Solving Maxwell's eqns. in empty space (4)
1
Notes:
1) solutions depend on both x and t!
2) E(x,t) and B(x,t) have same dependence on x and t!
3) (enforced by construction)
General Physics II, 171.102
Lecture 31
2
Maxwell's equations in matter
Maxwell's e
1
Electric Potential: basics
Electric Potential:
Property of fixed charges not
Integral independent of path closed path:
!
a scalar field
Unit: Volt
Potential of the single charge:
General Physics II, 171.102
[V] = joule / coulomb = 1 V
Lecture 9
2
Electr
Electric Potential: basics
Electric Potential:
Property of fixed charges not
1
Integral independent of path closed path:
!
a scalar field
Unit: Volt
Potential of the single charge:
General Physics II, 171.102
[V] = joule / coulomb = 1 V
Lecture 10
Potenti
1
Three types of materials
Isolators:
Conductors:
put the charge on them, it stays where it is
the charge can freely move
has important consequences (as we'll see soon)
example: charge deposited on conductors will usually spread
all over its surface
Semi
1
Maxwell's equations
So, finally, we have everything:
Gauss:
AmpereMaxwell:
Equations with sources.
Describe dynamics (equations of motion)
General Physics II, 171.102
Gauss for B, no monopoles:
Faraday:
Equations without sources.
Describe space.
Lectur
1
Maxwell's equations
So, finally, we have everything:
Gauss:
AmpereMaxwell:
Equations with sources.
Describe dynamics (equations of motion)
General Physics II, 171.102
Gauss for B, no monopoles:
Faraday:
Equations without sources.
Describe space.
Lectur
Energy of a dipole in E or B field
Electric dipole:
Rotate a dipole (
U of electric dipole:
General Physics II, 171.102
Magnetic dipole:
or
1
) store potential energy
U of magnetic dipole:
Lecture 18
2
BiotSavart Law
Sources of magnetic field:
permanent
Faraday's Law with
(Flux of B = Surface integral of B)
and
(emf = Contour integral of E)
General Physics II, 171.102
1
:
Use righthand rule by
convention
Faraday's law in
integral form:
Can tell us which way
emf is oriented!
Lecture 22
2
Lenz's Law
(incr
1
Energy stored in Electric Field
Work to move dq up the field:
But q and V are related via C:
+dq
Move dq from
1 to 2, one by
one
dq
+q
+dq
Start from both conductors
with q=0, and integrate
q
Keep moving
against the field.
General Physics II, 171.102
1
Magnetism
General Physics II, 171.102
(Lodestone
in the
Smithsonian)
Lecture 17
2
Early magnets
Lodestone: Greeks
or Chinese
First compass:
Han dinasty: divination
~ 1000 AD: navigation
lodestone: lead stone,
needle floating in water
Gilbert (1600): fir
1
Capacitance (3)
Double q V doubles. (Halve q V is halved, etc.)
q is proportional to V
CAPACITANCE
Capacitance:
property of the system (not the charge)
.i.e. of shapes and sizes of conductors
units: Farad, 1F = 1C/1V
General Physics II, 171.102
Lecture
1
Induced dipole moment
Clicker: the coke can will
A) be repulsed by charge rod
B) be attracted by charged rod
C) not move
General Physics II, 171.102
Lecture 8
2
Induced dipole moment
Clicker: the coke can will
A) be repulsed by charge rod
B) be attracte
1
Huygens' Principle
3dim transmission of waves (including light):
all points on a wavefront serve as point sources of spherical
secondary wavelets
after time t, new wavefront = envelope of secondary wavelets
General Physics II, 171.102
Lecture 33
2
Huyg
1
Interference from thin films
So far: path length difference phase difference
Another way to affect phase difference: reduce
e.g., light in an optically denser medium (n > 1)
For simplicity, let's ignore the
incidence angle and set it
to ~ 0.
Snell's law
1
Huygens' Principle
We already used it in the proof of Snell's Law:
Huygens' Principle
must satisfy boundary conditions
(continuous across the interface)
Envelope of
secondary wavelets
General Physics II, 171.102
Lecture 34
Diffraction
2
Plane wave hitti
Classical Physics 171.106
First Midterm Exam, March 1, 2004
PROBLEMS ARE ON BOTH SIDES OF PAGE! EXPLAIN
YOUR REASONING! Calculators are not needed or allowed.
Express all answers in terms of the variables dened in the
problem. You may use one 8.5x11 sheet
171.106: Electromagnetic Theory I
Midterm Exam 4/9/09 1:302:30
Check the attached formula page. Start each problem on a fresh page and please give
detailed reasoning. If in a later question you need a result from a question that you cannot
solve then wri
First Midterm
Physics 106
March 1, 2012
Do this exam by yourself. No calculators or books are needed or permitted. However,
a formula sheet (two pages of US letter size paper). Problems are on BOTH SIDES
of this page. Please explain your reasoning. Draw b
Final Exam
Physics 106
May 18, 2011
Do this exam by yourself. No calculators or books are needed or permitted. However,
a formula sheet (four pages of US letter size paper) is allowed. Problems are on BOTH
SIDES of this page. Please explain your reasoning