Lecture 42: FRI 05 DEC Final Exam Review

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Lecture 42 FRI 05 DECFinal Exam Review
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The Grading

• Midterms  -  100 points each
• Final Exam  -  200 points
• Homework   -  75 points
• In Class PP - 25 pointsTOTAL 600 points
• Numerical Grade Total Points / 6
• A 90100      B 7589      C 6074      D
  5059      F lt50

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Final Exam

• 530PM-730PM MON 08 DEC
• Cox Auditorium
• 50 of Exam From HW01-14
• 100 PTS CH 13, 2130
• 100 PTS CH 3133
• At least 1 Problem from Exam I, II, or III

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Final Exam

• 8 Questions 6 Problems
• Questions are labeled Question are multiple
  choice or similar and no partial credit.
• Problems are labeled Problem and you must show
  all your work to get any partial credit. In
  particular an answer in a problem with no
  explanation or no work will result in no credit.

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• What do you need to make on the final to get an
  A, B, C, etc.?
• A 90100      B 7589      C 6074      D
  5059      F lt50
• Solve this simple equation for x

Where mt1exam1, mt2exam2, mt3exam3, hwtotal
points on your hws0114 (out of 450),
icppcchecks, icppxXs, icppnumber of times you
were called on, max is the binary maximum
function, and y is your desired cutoff number, y
90, 75, 60, or 50. Then x is the score out of
200 you need on the final to make that cutoff
grade y. This assumes no curve.
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Example John Doe wants to know what he needs to
make on the final in order to get an A 90 in
this class.
It is very likely impossible for John to get an A
as hed need better than a perfect score on the
final. How good does he need to do to avoid a C
74?
John is extremely unlikely to get an A, and is
unlikely to get a C, so the most probable outcome
is that John will get a B in this class.
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LC Circuits
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PHYS2113 An Electromagnetic LC Oscillator
Capacitor initially charged. Initially, current
is zero, energy is all stored in the E-field of
the capacitor.
A current gets going, energy gets split between
the capacitor and the inductor.
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Electric Oscillators the Math
Amplitude ?
Voltage as Function of Time
Energy as Function of Time
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Example

• In an LC circuit, L 40 mH C
  4 µF
• At t 0, the current is a maximum
• When will the capacitor be fully charged for the
  first time?

• ? 2500 rad/s
• T period of one complete cycle
• T 2p/? 2.5 ms
• Capacitor will be charged after T1/4 cycle i.e
  at
• t T/4 0.6 ms

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Example

• In the circuit shown, the switch is in position
  a for a long time. It is then thrown to
  position b.
• Calculate the amplitude ?q0 of the resulting
  oscillating current.

• Switch in position a qCV (1 mF)(10 V) 10
  mC
• Switch in position b maximum charge on C q0
  10 mC
• So, amplitude of oscillating current

0.316 A
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Damped LCR Oscillator

• Ideal LC circuit without resistance oscillations
  go on forever ? (LC)1/2
• Real circuit has resistance, dissipates energy
  oscillations die out, or are damped
• Math is complicated! Important points
• Frequency of oscillator shifts away from
• ? (LC)-1/2
• Peak CHARGE decays with time constant
• tQLCR2L/R
• For small damping, peak ENERGY decays with time
  constant
• tULCR L/R

C
L
R
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Q(t)
t(s)
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Example, Transformer
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Displacement Current
Maxwell proposed it based on symmetry and math
no experiment!
i
i
E
Changing E-field Gives Rise to B-Field!
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Example, Magnetic Field Induced by Changing
Electric Field, cont.
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32.4 Displacement Current
Comparing the last two terms on the right side of
the above equation shows that the term must
have the dimension of a current. This product is
usually treated as being a fictitious current
called the displacement current id in which
id,enc is the displacement current that is
encircled by the integration loop. The charge q
on the plates of a parallel plate capacitor at
any time is related to the magnitude E of the
field between the plates at that time by in
which A is the plate area. The associated
magnetic field are AND
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Magnetic Moment vs. Magnetization
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32.10 Paramagnetism
The ratio of its magnetic dipole moment to its
volume V. is the magnetization M of the sample,
and its magnitude is In 1895 Pierre Curie
discovered experimentally that the magnetization
of a paramagnetic sample is directly proportional
to the magnitude of the external magnetic field
and inversely proportional to the temperature
T. is known as Curies law, and C is called
the Curie constant.
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Mathematical Description of Traveling EM Waves
All EM waves travel a c in vacuum
EM Wave Simulation
(33-5)
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The Poynting Vector Points in Direction of
Power Flow
Electromagnetic waves are able to transport
energy from transmitter to receiver (example
from the Sun to our skin).
The power transported by the wave and
its direction is quantified by the Poynting
vector.
John Henry Poynting (1852-1914)
For a wave, since E is perpendicular to B
In a wave, the fields change with time. Therefore
the Poynting vector changes too!! The direction
is constant, but the magnitude changes from 0 to
a maximum value.
Units Watt/m2
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EM Wave Intensity, Energy Density
A better measure of the amount of energy in an EM
wave is obtained by averaging the Poynting vector
over one wave cycle. The resulting quantity is
called intensity. Units are also Watts/m2.
The average of sin2 over one cycle is ½
Both fields have the same energy density.
The total EM energy density is then
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EM Spherical Waves
The intensity of a wave is power per unit area.
If one has a source that emits isotropically
(equally in all directions) the power emitted by
the source pierces a larger and larger sphere as
the wave travels outwards 1/r2 Law!
So the power per unit area decreases as the
inverse of distance squared.
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Example
A radio station transmits a 10 kW signal at a
frequency of 100 MHz. Assume a spherical wave. At
a distance of 1km from the antenna, find the
amplitude of the electric and magnetic field
strengths, and the energy incident normally on a
square plate of side 10cm in 5 minutes.
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Radiation Pressure
Waves not only carry energy but also momentum.
The effect is very small (we dont ordinarily
feel pressure from light). If light is completely
absorbed during an interval ?t, the momentum
Transferred ?p is given by
F
and twice as much if reflected.
A
Newtons law
I
Now, supposing one has a wave that hits a
surface of area A (perpendicularly), the amount
of energy transferred to that surface in time ?t
will be
therefore
Radiation pressure
PaN/m2
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EM waves polarization
Radio transmitter
If the dipole antenna is vertical, so will be the
electric fields. The magnetic field will
be horizontal.
The radio wave generated is said to be
polarized.
In general light sources produce unpolarized
wavesemitted by atomic motions in random
directions.
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EM Waves Polarization
Completely unpolarized light will have equal
components in horizontal and vertical directions.
Therefore running the light through a polarizer
will cut the intensity in half II0/2
When polarized light hits a polarizing
sheet, only the component of the field aligned
with the sheet will get through.
And therefore
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Example
Initially unpolarized light of intensity I0 is
sent into a system of three polarizers as shown.
What fraction of the initial intensity emerges
from the system? What is the polarization of the
exiting light?

• Through the first polarizer unpolarized to
  polarized, so I1½I0.
• Into the second polarizer, the light is now
  vertically polarized. Then, I2 I1cos2(60o) 1/4
  I1 1/8 I0.
• Now the light is again polarized, but at 60o.
  The last polarizer is horizontal, so I3
  I2cos2(30o) 3/4 I2 3 /32 I0 0.094 I0.
• The exiting light is horizontally polarized, and
  has 9 of the original amplitude.

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