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Question

A coil of radius R carries a current I. Another concentric coil of radius r(r<<R) caries current I2. Initially planes of the two coils are mutually perpendicular and both the coils are free to rotate about common diameter. They are released from rest from this position. The masses of the coils are M and m respectively (m<M). During the subsequent motion let K1 and K2 be the maximum kinetic energies of the two coils respectively and let U be the magnitude of maximum potential energy of magnetic interaction of the system of the coils. Choose the correct options.

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Solution

The correct option is **A** U=μ0πI2r24R

K.E=12Iw2 (1)

Coil 1 | Coil 2 | |

Radius | R | r(<<R) |

Current | I | I/2 |

Mass | M | m |

Kinetic energy | K1 | K2 |

∴K−1=12×Iw2⟹I∝1K.E

K2=MR22w2

Now K1/K2=mm(rR)2 and K1+K2=U (ii)

⟹K2×mM(r/R)2+K2=U

⟹K2=UMR2mr2+MR2

Similarly K1=UMR2mr2+MR2

And using (ii)

U=U=12πr2μ2I2R=μ2I2πr24R=U

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