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chp34_5 - then Φ B = BA and ε =-d Φ B/dt =-A dB/dt = π...

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PHY2061 R. D. Field Department of Physics chp34_5.doc University of Florida Lenz’s Law Example ( Loop of Wire in a Changing Magnetic Field ): A wire loop with a radius, r , of 1 meter is placed in a uniform magnetic field. Suppose that the electromagnetic is suddenly switched off and the strength of the magnetic field decreases at a rate of 20 Tesla per second . What is the induced EMF in the loop (in Volts)? If the resistance of the loop, R, is 5 Ohms, what is the induced current in the loop (in Amps)? What is the direction of the induced current? What is the magnitude and direction of the magnetic field produced by the induced current ( the induced magnetic field ) at the center of the circle? Answers: If I choose my orientation to be counterclockwise
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Unformatted text preview: then Φ B = BA and ε = -d Φ B /dt = -A dB/dt = -( π r 2 )(-20T/s) = 62.8 V . The induced current is I = ε /R = (62.8 V)/(5 Ω ) = 12.6 A . Since ε is positive the current is flowing in the direction of my chosen orientation ( counterclockwise ). The induced magnetic field at the center of the circle is given by B ind = 2 π kI/r = (2 π x 10-7 Tm/A)(12.6 A)/(1 m) = 7.9 µ T and points out of the paper . Lenz’s Law: It is a physical fact not a law or not a consequence of sign conventions that an electromagnetic system tends to resist change. Traditionally this is referred to as Lenz’s Law: Induced EMF’s are always in such a direction as to oppose the change that generated them. B-out changing with time r Loop...
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