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A rod PQ of length 1 is moved in uniform magnetic field \vec{B} as shown. What will be the emf induced in it? |
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Answer» The maximum emf induced in the coil will beExplanation:32 Tπ 2 NB 0 (a 2 +ab+b 2 ) The number of turms in he spiral coil per unit radial width n= b−aN The emf induced in an 'almost circular' part of spiral at radial DISTANCE r is dV= dtdϕ = dtd(nB.πr 2 ) =nB 0 T2π cos( T2π t)πr 2 Since these are almost circular, but actually end to end connected, each of these rings at radial distances varying from a to b would add up to given total emf ACROSS the loop.Hence V=∫ ab nB 0 T2π cos( T2π t)πr 2 dr= 32 Tπ 2 NB 0 (a 2 +ab+b 2 ) cos( T2π t) [Since (b 3 −a 3 )=(b−a)(a 2 +ab+b 2 )]Thus the maximum VALUE of the emf is= 32 Tπ 2 NB 0 (a 2 +ab+b 2 ) |
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