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Unformatted text preview: Physics 227:
Exam 2 Information • Note: exam 2: 16 questions covering chapters 25  28 •
• •
• Thursday, Nov 17, 2011, 9:40 PM  11:00 PM
Room assignments: • AI Arc 103
• JM SEC 111  probably starts 9:50 or 10:00.
• NR PLH
• SZ Beck Auditorium, Livingston Campus!!! (NOT Hill 114) Anyone with a conﬂict should contact Prof. Cizewski ASAP
Bring pencils, 1 formula sheet w/ anything you want, NO
calculators or other electronics needed or allowed! Thursday, November 10, 2011 Physics 227: Lecture 19
Comments on Electric Fields,
Eddy Currents, Superconductivity • Lecture 18 review: •
•
•
•
• Faraday’s Law: ε =  dφB/dt.
Lenz’s Law: ε o pposes change.
Alternators.
Generators.
Motional emf. Thursday, November 10, 2011 Today: lots of nice demos! Superconducting iClicker
The emf, when the loop
shown is pulled out of the
magnetic ﬁeld region, is ε =
0.4x0.02xB V CW. Usually I
=V
/R. But if the loop is
superconducting, what is the
current in it?
A. ε / R = ε / 0 = ∞ A.
B. It cannot be ∞, so it must be 0. The superconductor is
not special  there
w ill be an emf and
non∞ current, but we
do not know how to
calculate it.
Thursday, November 10, 2011 C. Because it is a superconductor, ε = 0 and I = 0.
D. It is some number between 0 and ∞ that we
do not know how to calculate.
E. It is some number between 0 and ∞ that
cannot be calculated in principle  it is random. Maxwell’s Equations
In the late 1800s the knowledge of electric and magnetic ﬁelds was
summarized with Maxwell’s Equations: ρ
∇·E =
0
∇·B =0
∂B
∇×E =−
∂t qenclosed
E · dA =
0
There are no magnetic
B · dA = 0
Gauss’s Law: electric
ﬁelds start/stop on
charges.
charges.
Changing magnetic
dφB
s
ﬁelds generate electric
E · d = −
dt
ﬁelds. Today! Magnetic ﬁelds result
∂E
× B = µ0 0
from currents and
∇
+ µ0 J
changing electric ﬁelds.
∂t
1 dφE
s
+ µ0 ienc
B · d = 2
c dt Thursday, November 10, 2011 EMF And Electric Fields
We have now seen that there are two different origins for
electric ﬁelds, that lead to two different types of ﬁelds.
We ﬁrst learned that charge distributions lead to electric
ﬁelds that start / stop on the charges. These electric ﬁelds
are derivatives / slopes of voltages, so the line integral of E.dl
is the voltage difference.
We now also know that changing magnetic ﬁelds lead to emfs
and electric ﬁelds with a different conﬁguration. The resulting
electric ﬁeld does not start or stop on a charge. Instead, like
w ith magnetic ﬁelds, these electric ﬁelds curl around and form
a closed loop. Here the line integral of E.dl around a closed
loop is dφB/dt, but can be arbitrary if the loop is not closed.
It is not 0, as it would be if charges were generating the
electric ﬁeld. Thursday, November 10, 2011 Faraday’s Law iClicker
x x
x
solenoid
x A. 0 V.
B. A (dB/dt) V.
C. A (dB/dt) V.
D. (A/2) (dB/dt) V.
E. (A/2) (dB/dt) V.
Thursday, November 10, 2011 +
V
 The current in an ideal solenoid of area A in
increasing so that the ﬁeld increases into the
page at a rate dB/dt. This induces an emf in a
loop around the solenoid.
What voltage does the voltmeter hooked up
as shown measure? An emf is not a voltage.
For the emf around the loop, there is no
reason to think it is more positive on one side
than the opposite side  the cylinder part of
the probelm is rotationally symmetric. Induced Field / Emf Applications Magnetic regions on
spinning disk cause
electric signal in
pickup coil. Regenerative braking
in hybrid car
charges batteries. Engine rotation
powers spark in
airplane engine. A large set of applications will be covered next week, under the
topic of ``inductance’’. Thursday, November 10, 2011 Eddy Currents
Motion of a conductor
through a region of varying
magnetic ﬁelds leads to
e ddy currents circulating
around within the
conductor. Finite resistance
heats the conductor up
w ith power P = I2R. Thursday, November 10, 2011 Eddy Currents
The eddy currents form
patterns, as shown here.
If the disk is rotating freely,
its mechanical energy is
converted to heat and it
slows up. You can see that
the direction of the
magnetic force on the
currents, IdlxB, is to the
right, opposing the rotation
of the disk. This effect leads
to several applications for
e ddy currents. And some
nice demos. Thursday, November 10, 2011 Eddy Current Applications
Braking of rotational motion.
Metal detectors.
Heating materials without mechanical
contact (induction heating). Thursday, November 10, 2011 Eddy Current Applications
Motion of Io through Jupiter’s
magnetic ﬁeld leads to eddy
currents.
Io has a liquid magma ocean,
which can conduct large
currents.
http:/
/www.nasa.gov/topics/
solarsystem/features/
galileo20110512.html Thursday, November 10, 2011 Magnets Moving Near Conductors
Generally, if I have magnets moving near conductors, or
conductors moving near magnets, there are eddy currents which
can convert mechanical energy into electric currents, which
through P=I2R heat the conductor.
Let’s see some examples!
Why did the can implode?
What happens if we put the can in offcenter?
Which disk slowed up the most? ... the least? Why?
Is gravity different in the tube?
Why does one ring jump and not the other? Thursday, November 10, 2011 Superconductors Field expelled from body of superconductor.
TC depends on external ﬁeld.
Thursday, November 10, 2011 Demo  done a while ago Thursday, November 10, 2011 Applications Magnetic levitation trains
SQUIDS: Superconducting QUantum Interference Devices
Electromagnets
Power transmission Thursday, November 10, 2011 Eddy Current iClicker
In what order do the disks race through a magnetic ﬁeld? Insulator Conductor Conductor
w ith holes Conductor
w ith slots B. I, Ch, Cs, C. Ignore changes to the moment of inertia.
Assume the B ﬁeld is constant and the same
size as the disks. C. C, Ch, Cs, I. We saw this in demo. A. I, Cs, Ch, C. D. C, Cs, Ch, I.
E. I, Cs, C, Ch.
Thursday, November 10, 2011 Thank you.
Prof. Cizewski will be giving
the lecture Monday, Nov 14,
and a review for the exam on
Thursday Nov 17. Thursday, November 10, 2011 ...
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This note was uploaded on 01/03/2012 for the course PHYSICS 750:227 taught by Professor Ronaldgilman during the Fall '11 term at Rutgers.
 Fall '11
 RonaldGilman
 Physics

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