Physics-
General
Easy

Question

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

  1. 10– 4 A (Clockwise), 2 cross times 10 to the power of negative 4 end exponent A (Clockwise)    
  2. 10– 4 A (Anticlockwise), 2 cross times 10– 4 A (Clockwise)    
  3. 2 cross times 10– 4 A (clockwise), 10– 4 A (Anticlockwise)    
  4. 2 cross times 10– 4 A (Anticlockwise), 10– 4 A (Anticlockwise)    

The correct answer is: 10– 4 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 1 0 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 1 0 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 1 0 to the power of negative 3 end exponent equals 1 0 to the power of negative 4 end exponent A
    According to lenz’s law direction of i1 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 1 0 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 1 0 to the power of negative 3 end exponent equals 2 cross times 1 0 to the power of negative 4 end exponent A   left parenthesis C W right parenthesis

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