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Q.

Plane figures made of thin wires of resistance R = 50 milli ohm/meter are located in a uniform magnetic field perpendicular to the plane of the figures and whichdecrease at the rate dB/dt = 0.1 mT/s. Then currents in the inner and outer boundary are (The inner radius a = 10 cm and outer radius b = 20 cm)

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a

10−4A (Clockwise), 2×10−4A (Clockwise)

b

10−4A (Anticlockwise), 2×10−4A (Clockwise)

c

2×10−4A (clockwise), 10−4 . A (Anticlockwise)

d

2×10−4A (Anticlockwise), 10−4A (Anticlockwise)

answer is A.

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Detailed Solution

Current in the inner coil i1=εR=A1R1dBdtLength of the inner coil=2πaSo its resistance R1=50×10−3×2π(a)∴ i1=πa250×10−3×2π(a)×0.1×10−3=10−4A According to Lenz's law, direction of il is clockwise. Induced current in outer coil i2=ε2R2=A2R2dBdt⇒ i2=πb250×10−3×(2πb)×0.1×10−3=2×10−4A(CW)

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Plane figures made of thin wires of resistance R = 50 milli ohm/meter are located in a uniform magnetic field perpendicular to the plane of the figures and whichdecrease at the rate dB/dt = 0.1 mT/s. Then currents in the inner and outer boundary are (The inner radius a = 10 cm and outer radius b = 20 cm)