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Physics-

General

Easy

Question

Plane figures made of thin wires of resistance $R plus 50 blank m i l l i blank o h m divided by m e t r e$ are located in a uniform magnetic field perpendicular into the plane of the figures and which decrease at the rate $d B divided by d t equals 0.1 blank m blank T divided by s$ . The current in the inner and outer boundary are inner radius $a equals 10 blank c m$ and outer radius $b equals 20 blank c m$ )

$10^{- 4} A$ (Clockwise), $2 \times 10^{- 4} A$ (Clockwise)
$10^{- 4} A$ (Anticlockwise), $2 \times 10^{- 4} A$ (Clockwise)
$2 \times 10^{- 4} A$ (Clockwise), $10^{- 4} A$ (Anticlockwise)
$2 \times 10^{- 4} A$ (Anticlockwise), $10^{- 4} A$ (Anticlockwise)

The correct answer is: $10 to the power of negative 4 end exponent A$ (Clockwise), $2 cross times 10 to the power of negative 4 end exponent A$ (Clockwise)

Current in the inner coil $i equals fraction numerator e over denominator R end fraction equals fraction numerator A subscript 1 end subscript over denominator R subscript 1 end subscript end fraction fraction numerator d B over denominator d t end fraction$
Length of the inner coil $equals 2 pi a$
So it’s resistance $R subscript 1 end subscript equals 50 cross times 10 to the power of negative 3 end exponent cross times 2 pi left parenthesis a right parenthesis$
$therefore i subscript 1 end subscript equals fraction numerator pi a to the power of 2 end exponent over denominator 50 cross times 10 to the power of negative 3 end exponent cross times 2 pi left parenthesis a right parenthesis end fraction cross times 0.1 cross times 10 to the power of negative 3 end exponent equals 10 to the power of negative 4 end exponent A$
According to lenz’s law direction of $i subscript 1 end subscript$ is clockwise
Induced current in outer coil $i subscript 2 end subscript equals fraction numerator e subscript 2 end subscript over denominator R subscript 2 end subscript end fraction equals fraction numerator A subscript 2 end subscript over denominator R subscript 2 end subscript end fraction fraction numerator d B over denominator d t end fraction$
$rightwards double arrow i subscript 2 end subscript equals fraction numerator pi b to the power of 2 end exponent over denominator 50 cross times 10 to the power of negative 3 end exponent cross times left parenthesis 2 pi b right parenthesis end fraction cross times 0.1 cross times 10 to the power of negative 3 end exponent equals 2 cross times 10 to the power of negative 4 end exponent A left parenthesis C W right parenthesis$

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