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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.