problem29_49

problem29_49 - 29.49:a) (i) | | d dt B d B Consider a...

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29.49: a) (i) dt d B Φ = | | ε Consider a narrow strip of width dx and a distance x from the long wire. The magnetic field of the wire at the strip is . 2 0 x I B π μ = The flux through the strip is ) / ( ) 2 ( 0 x dx Ib Bbdx d B = = Φ The total flux through the loop is + = Φ = Φ a r r B B x dx Ib d 2 0 ) ( 2 | | ) ( 2 a ln 2 0 0 0 a r r Iabv v a r r a Ib dt dr dt d dt d r r lb B B B + = + - = Φ = Φ + = Φ (ii) Bvl = for a bar of length l moving at speed v perpendicular to magnetic field . B The emf in each side of the loop is
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0 , ) ( 2 , 2 4 2 0 2 0 1 = = + = = ε π μ vb a r I vb r I Both emfs 2 1 and are directed toward the top of the loop so oppose each other. The net emf is ) ( 2 1 1 2 0 0 2 1 a r r Iabv a r r Ivb μ + = + - = - = This expression agrees with what was obtained in (i) using Faraday’s law. b) (i) Φ is . is B B and decreasing, so the flux ind Φ of the induced current is
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This homework help was uploaded on 02/03/2008 for the course PHYS 208 taught by Professor Ross during the Spring '08 term at Texas A&M.

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problem29_49 - 29.49:a) (i) | | d dt B d B Consider a...

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