Faraday’s Law cos B B where BA BA t • 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)
Dec 19, 2015
Faraday’s Law
cosBBwhere B A BA
t
• 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 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).
a) What is the B field at the loop?b) What is the magnetic flux through the loop?c) 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.
d) 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.
SQUID noise
10-4
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10-8
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B field (T)
Earth’s field
Urban B noise
heart
eye
brain
car at 50 m
screwdriver at arms length
transistor at 1 m
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?
(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.
(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.