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Faraday’s Law
 B
 
t
where  B  B A  BA cos 
•  produces an induced current
• Lenz’s Law: Induced current is in a direction so as to
produce a B opposing the change in magnetic flux, B,
that creates it (to conserve energy)
Group Problems
1.
a)
b)
c)
d)
A long straight vertical wire has a 5A current flowing
upwards. A small loop, 2mm x 2mm, lies 1m from the
wire lying in a plane with the wire (with its normal
perpendicular to that common plane).
What is the B field at the loop?
What is the magnetic flux through the loop?
If at t = 0, the loop is moved from its initial position to a
distance of 5m from the wire at t = 2s, without any
change in its orientation, find the averaged induced
emf in the loop during this time.
If the loop has a 10 ohm resistance, what is the
average induced current in the loop during this time?
After this time, when the loop is at 5m from the wire?
Second Group Problem
•
Suppose that in the circuit above the thick rod has a
length of 20 cm and a resistance of 500 ohms and is
free to move (without friction) along the track of thin
wire (with ~0 resistance), completing a loop circuit. If
there is a uniform 2 T B field everywhere into the page,
and the rod is pulled to the right at a speed of 5 m/s
a) Find the rate of change of the magnetic flux through the
circuit.
b) Find the induced current in the circuit and its direction
through the rod.
Basis of an electric generator
Microphone (or speaker)
Reading Magnetic Tape
B field (T)
10-4
Earth’s field
10-5
10-6
Urban B noise
10-7
10-8
car at 50 m
10-9
screwdriver at arms length
transistor at 1 m
10-10
heart
10-11
eye
10-12
brain
10-13
10-14
SQUID noise
10-15
Magneto-encephalography
MEG false color recording (left) of brain response
to hearing pure tone, (center) superimposed on
MRI cross-section of the brain. Right is the
mapping of the MEG signal used to generate the
false color recording.
Gradiometer with two coils that cancel out distant spatially
constant B fields. Note the direction of the induced current
flow in the two coils – do you see how it works?
A SQUID detector, several cm on a side, made using thin film
technology.
Magnetic moment for NMR
z
B
Spin up
Spin down
NMR block diagram
Detector
N
Recorder
S
sample
RF Source
(bottom) Single proton NMR scan of a sample of the female sex
hormone, progesterone; (top, with reduced amplitude) the sum of 500
scans showing the vast improvement in the signal-to-noise ratio
(a) The direct FT NMR signal from acetaldehyde, CH3CHO and (b) a portion
of its spectrum, obtained by taking the Fourier Transform of (a). Note the
methyl quartet structure for the OH proton.
An MRI machine used for whole-body medical imaging. (Courtesy GE
Medical Systems)
(left) Field gradient established by gradient coil; (right) signal detected if there
were only 3 equivalent “proton centers” in the patient’s head (shown in red) –
note that only two peaks are seen because of the variation in resonance
position along the field gradient, one with twice the integrated intensity of the
other.