910_Physics ProblemsTechnical Physics

910_Physics ProblemsTechnical Physics - 250 *P32.44...

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250 Inductance *P32.44 The large coil produces this field at the center of the small coil: NI R xR 1011 2 2 1 2 32 2 µ + ej . The field is normal to the area of the small coil and nearly uniform over this area, so it produces flux Φ 12 2 2 1 2 2 2 2 = + R R π through the face area of the small coil. When current I 1 varies, this is the emf induced in the small coil: ε µπ πµ 22 101 2 2 2 2 1 2 1 12 01 2 2 2 2 1 2 11 =− + + N d dt NR R I NN RR dI dt M dI dt so M = + 2 2 2 2 1 2 2 . P32.45 With II I =+ 12 , the voltage across the pair is: VL dI dt M dI dt L dI dt M dI dt L dI dt 1 2 21 eq . So, −=+ dI dt V L M L dI dt 1 2 and −+ + = L dI dt MV L M L dI dt V 2 2 1 2 1 2 a f (a) (b) FIG. P32.45 = LL M dI dt M 2 2 1 bg . [1] By substitution, dI dt V L M L dI dt 2 1 leads to = M dI dt M 2 1 2 . [2] Adding [1] to [2],
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This note was uploaded on 12/14/2011 for the course PHY 203 taught by Professor Staff during the Fall '11 term at Indiana State University .

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