4B_SP10_con11_31 - Physics 4B Spring 2010 Conference # 11...

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Unformatted text preview: Physics 4B Spring 2010 Conference # 11 – Electromagnetic Induction 1. A rod with length L, mass m, and resistance R slides without friction down parallel conducting rails of negligible resistance, as shown in the figure. The rails are connected together at the bottom as shown, forming a conducting loop with the rod as the top member. The plane of the rails makes an angle θ with the horizontal, and a uniform vertical magnetic field B exists throughout the region. Show that the rod reaches a terminal velocity of magnitude v= mgR sin θ B 2 L2 cos 2 θ 2. (Ch. 31, Problem 2) A long, straight wire carries a constant current I. A metal rod of length moves at constant velocity on rails of negligible resistance that terminate in a dΦm resistor R, as shown in Fig. 31.50. Use E = − to find the induced emf in the resistor. dt Compare this to the result found from using E = ∫ ( v × B ) ⋅ d . 3. (Ch. 31, Problem 1) A long, straight wire carries a constant current I. A metal rod of length L moves at velocity v relative to the wire, as shown in Fig. 31.49. What is the potential difference between the ends of the rod? (Note that the field is not uniform.) Useful equations: F = IL × B E=− dΦm dt E= ∫ (v × B ) ⋅ d Answers: µ0 ILv µ Iv L + d 2. , 3. 0 ln 2π ( d + a ) 2π d ...
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