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Solutions6 - Physics 208 Assignment 6 Solutions RT Problem...

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Physics 208, Assignment 6, Solutions, 3/1/09, RT Problem 1. The normal vector is chosen normal to the coil but arbitrarily as regards up or down. But then the positive current sense has to be matched by the right hand rule (thumb along ˆn , fingers along positive sense). The resulting positive sense is shown. B n θ positive current sense positive rotation sense a axis of rotation (a) The flux through the square loop is Φ( θ ) = integraldisplay integraldisplay B · ˆn dA. = Ba 2 cos θ. (The two integral signs imply area (2D) integration.) (b) Corresponding to N revolutions per second, the radian frequency is ω = 2 πN . The coil angle and flux through loop are given by θ = ωt, and Φ( t ) = Ba 2 cos ωt. (c) The induced e.m.f. is E = d Φ dt = Ba 2 ω sin ωt. Note that positive E causes current to flow in the positive sense. This would be the case during the first half cycle after t = 0. 1
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Problem 2. The loop shown moves inexorably from outside to inside a mag- netic field region. (This could only happen if some external agent is over- coming gravitational and magnetic forces.) While outside the field region there is no e.m.f. because there is no flux linking the loop. Set the time origin t = 0 at the instant the leading edge of the coil is aligned with the field edge. B = 0 B = 0 / n L L z v vt positive current sense B (a) With the loop partially in the magnetic field as shown, current is induced. By Lenz’s law the current flows in the sense that opposes the increase in flux. The induced field therefore points out of the page
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