Maxwells Equations and Electromagnetic Waves
Challenge Problem Solutions
Problem 1:
The magnetic field of a plane electromagnetic wave is described as follows:
B = B0 sin( kx t )
j
a) What is the wavelength of the wave?
b) Write an expression for the ele
Capacitors and Dielectrics
Challenge Problems
Problem 1:
A parallel plate capacitor has capacitance C. It is connected to a battery of EMF until
fully charged, and then disconnected. The plates are then pulled apart an extra distance d,
during which the m
Capacitors and Dielectrics
Challenge Problem Solutions
Problem 1:
A parallel plate capacitor has capacitance C. It is connected to a battery of EMF until
fully charged, and then disconnected. The plates are then pulled apart an extra distance d,
during wh
Angular Momentum Problems
Challenge Problems
Problem 1: A spaceship is sent to investigate a planet of mass mp and radius rp . While
hanging motionless in space at a distance 5rp from the center of the planet, the ship fires
an instrument package with spe
Module
Module 04: Electric Fields and
Continuous Charge
Distributions
1
Continuous Charge Distributions
Break distribution into parts:
V
Q = qi
i
dq
V
E field at P due to q
r
r
q
dq
E = ke 2 r d E = ke 2 r
r
r
Superposition:
r
E(P) = ?
r
r
r
E = E dE
2
Module 29:
Energy and Momentum in
EM Waves
1
Module 29: Outline
Energy and Momentum in EM Waves
2
Summary:
Traveling Electromagnetic
Waves
3
Properties of EM Waves
Travel (through vacuum) with
speed of light
v=c=
m
= 3 10
s
0 0
1
8
At every point in the w
Module 24:
Undriven RLC Circuits
1
Module 24: Outline
Undriven
Undriven RLC Circuits
Expt. 8: Part 2:Undriven RLC
Circuits
2
Circuits
Circuits that Oscillate (LRC)
3
Mass on a Spring:
Simple Harmonic Motion
(Demonstration)
4
Mass on a Spring
(1)
(2)
What
Module 27:
Poynting Vector and
Energy Flow
1
Module 27: Outline
Poynting
Poynting Vector and Energy Flow
Examples
2
Energy Flow
3
Poynting Vector
Power flow per unit area:
rr
r EB
S=
: Poynting vector
0
4
Problem: Resistor Power
a
I
L
Consider the above c
Module 23:
LR
LR Circuit
1
Module 23: Outline
LR
LR Circuits
Expt. 8: Part 1: LR Circuits
2
Think Harder about Faraday
3
Concept
Concept Question Question:
Faraday in Circuit
4
Concept Question: Faraday Circuit
A magnetic field B penetrates this
circuit o
Module 32:
Diffraction
Diffraction
1
Module 32: Outline
Diffraction
Diffraction
Experiment 11: Interference and
Diffraction
2
Diffraction
3
Diffraction
Diffraction: The bending of waves as they pass by
certain obstacles
No Diffraction
Diffraction
No sprea
Module 25:
Driven RLC Circuits
1
Module 25: Outline
Resonance
Resonance & Driven LRC Circuits
2
Driven Oscillations:
ill ti
Resonance
Resonance
3
Mass on a Spring:
Simple Harmonic Motion
A Second Look
4
Mass on a Spring
(1)
(2)
We solved this:
2
(3)
(4)
d
Module 2: Math Review
A. Vector Analysis
A.1 Vectors
A.1.1 Introduction
Certain physical quantities such as mass or the absolute temperature at some point only
have magnitude. These quantities can be represented by numbers alone, with the
appropriate unit
Module 31:
Interference
Interference
1
Module 31: Outline
Interference
Interference
2
How in the world do we
measure
measure 1/10,000 of a cm?
Visible (red) light:
f red = 4.6 10 Hz red
14
c
5
= = 6.54 10 cm
f
3
We
We Use Interference
This is also how we
Concept Question: Wave
(m)
The graph shows a plot of the function
y = cos(k x). The value of k is
1.
2.
3.
4.
5.
m1
m1
m1
/2 m1
I dont know
1
Concept Question: Direction of
Propagation
The figure shows the
E (yellow) and B (blue)
fields of a plane
Module
Module 18:
Magnetic
Magnetic Dipoles
1
Module 18: Outline
Magnetic Dipoles
po
Magnetic Torques
2
Magnetic Dipole Moment
r
r
IAn IA
3
Torque on a Current Loop in a
Uniform Magnetic Field
4
Problem: Current Loop
Place rectangular current loop in uni
Module 19:
Sources of Magnetic Fields:
BiotSavart Law
1
Module 19: Outline
Magnetic Fields, Creating Fields:
BiotSavart Law
2
Sources of Magnetic Fields
3
What creates fields?
Magnets more about this later
The Earth Hows that work?
Moving charges!
4
Ele
Module
Module 06: Electric Potential
Discrete and Continuous
Distributions of Charge
1
Summary:
Gravitational
Gravitational & Electric Fields
2
Summary: Gravity  Electricity
SOURCE:
Mass Ms
Charge qs ()
CREATE:
r
Ms
g = G 2 r
r
r
qs
E = ke 2 r
r
r
r
Fg =
Module
Module 07: Electric Potential;
Equipotential Lines and Electric
Fields
1
Module 07: Outline
Electric
Electric Potential
Lab 1: Equipotentials
ab
po
2
Last Time:
Potential
Potential and E Field
3
E Field and Potential: Creating
A point charge q crea
Module 09: Conductors and
09
Insulators; Conductors as
Insulators; Conductors as
Shields
1
Conductors
2
Conductors and Insulators
Conductor: Charges are free to move
Electrons
Electrons weakly bound to atoms
Example: metals
Insulator: Charges are NOT free
Module 05: Gausss Law
odu
1
Gausss Law
The first Maxwell Equation!
And a very useful computational technique to find
th
the electric field E w hen the source has enough
ld
symmetry.
2
Gausss Law The Idea
Th
The total flux of field lines penetrating any of
Module 01:
Introduction to
Electric Fields
1
Scalar Fields
e.g. Temperature: Every location has
associated value (number with units)
2
Scalar Fields  Contours
Colors represent surface temperature
Contour lines show constant temperatures
3
Fields are 3D
Module
Module 11: Capacitors and
Dielectrics
P11 1
Demonstration:
Demonstration:
Dissectible Capacitor
P11 2
Dielectrics
A dielectric is a nonconductor or insulator
conductor
Examples: rubber, glass, waxed paper
When
When placed in a charged capacitor,
Module 10: Capacitance
P09  1
Capacitors and Capacitance
Our
Our first of 3 standard electronics devices
(Capacitors, Resistors & Inductors)
P09  2
Capacitors: Store Electric Charge
Capacitor: Two isolated conductors
Equal and opposite charges Q
Potenti
Module 16: Magnetic Fields
1
Module 16: Outline
Magnetic
Magnetic Field
2
Magnetic Fields
3
Magnetic Field of Bar Magnet
(1) A magnet has two poles, North (N) and South (S)
(2) Magnetic field lines leave from N, end at S
4
Magnetic
Magnetic Field of the E
Module
Module 13: Batteries and
Circuit Elements
1
Class 13: Outline
DC Circuits and Kirchhoffs Loop
Rules
2
Batteries
Batteries &
Elementary Circuits
3
DC Circuits
4
Examples of Circuits
it
5
Symbols for Circuit Elements
Battery
Resistor
Resistor
Capacit
Module 17:
Magnetic Forces
1
Module 17: Outline
Magnetic Forces on Charges
ces
ges
2
Recall:
ll
Cross
Cross Product
3
Notation Demonstration
XXXX
XXXX
XXXX
XXXX
OUT of page
Arrow Head
INTO page
Arrow Tail
4
Cross Product: Magnitude
Computing magnitude of
Module
Module 15: DC Circuits with
Capacitors
1
Modules 15: Outline
Capacitors
Capacitors in Series and Parallel
RC Circuits
cu
Expt 4: RC Circuits
2
DC Circuits with Capacitors
3
Sign Conventions  Capacitor
Moving across a capacitor from the negatively
Simple and Physical Pendulums
Challenge Problems
Problem 1: Pendulum
A simple pendulum consists of a massless string of length l and a pointlike object of
mass m attached to one end. Suppose the string is fixed at the other end and is initially
pulled out
Concept Question: Dielectric
A parallel plate capacitor is charged to a total charge
Q and the battery removed. A slab of material with
dielectric constant in inserted between the plates.
The charge stored in the capacitor
+

1. Increases
2. Decreases
3.