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Q.

A conducting disc of conductivity σ has radius a and thickness δ . A uniform magnetic field B→ is applied in a direction perpendicular to the plane of the disc. Thecylindrical region of the magnetic field is coaxial with the disc. If the magnetic field changes with time at the rate of dB/dt, then the power dissipated in the disc due to theinduced current is?

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a

πδσa48dBdt2

b

πδσa412dBdt2

c

πδσa44dBdt2

d

πδσa46dBdt2

answer is A.

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Detailed Solution

ε=πr2dBdtdR=2πrσδdrdP=ε2dR=πδσ2dBdt2r3drP=πδσa48dBdt2
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A conducting disc of conductivity σ has radius a and thickness δ . A uniform magnetic field B→ is applied in a direction perpendicular to the plane of the disc. Thecylindrical region of the magnetic field is coaxial with the disc. If the magnetic field changes with time at the rate of dB/dt, then the power dissipated in the disc due to theinduced current is?