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Wave Optics

Question
CBSEENPH12039509

A circular loop of radius 0.3 cm lies parallel to a much bigger circular loop of radius 20 cm. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is 15 cm. If a current of 2.0 A flows through the smaller loop, then the flux linked with bigger loop is 

  • 9.1 x 10-11 Wb

  • 6 x 10-11 Wb

  • 3.3 x 10-11 Wb

  • 6.6 x 10-9 Wb

Solution

A.

9.1 x 10-11 Wb


Let M12 be the coefficient of mutual induction between loops
straight capital phi subscript 1 space equals space straight M subscript 12 space straight i subscript 2
rightwards double arrow space fraction numerator straight mu subscript 0 straight i subscript 2 straight R squared over denominator 2 left parenthesis straight d squared plus straight R squared right parenthesis to the power of 3 divided by 2 end exponent end fraction πr squared space equals space straight M subscript 12 space straight i subscript 2
rightwards double arrow space straight M subscript 12 equals space fraction numerator straight mu subscript 0 straight R squared over denominator 2 left parenthesis straight d squared plus straight R squared right parenthesis to the power of 3 divided by 2 end exponent end fraction πr squared space
straight capital phi space equals space straight M subscript 12 space straight i subscript 1
rightwards double arrow straight capital phi subscript 2 space equals space 9.1 space straight x space 10 to the power of negative 11 end exponent space weber

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