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Easy

Question

A pair of parallel conducting rails lie at right angle to a uniform magnetic field of 2.0 T as shown in the fig. Two resistors 10 W and 5 capital omega are to slide without friction along the rail. The distance between the conducting rails is 0.1 m. Then

  1. Induced current equals fraction numerator 1 over denominator 150 end fraction A directed clockwise if 10 capital omega resistor is pulled to the right with speed 0.5 ms–1 and 5 capital omega resistor is held fixed    
  2. Induced current equals fraction numerator 1 over denominator 300 end fraction A directed anti-clockwise if 10 capital omega resistor is pulled to the right with speed 0.5 ms–1 and 5 capital omega resistor is held fixed    
  3. Induced current equals fraction numerator 1 over denominator 300 end fraction A directed clockwise if 5 capital omega resistor is pulled to the left at 0.5 ms–1 and 10 capital omega resistor is held at rest    
  4. Induced current equals fraction numerator 1 over denominator 150 end fraction Adirected anti-clockwise if 5 capital omega resistor is pulled to the left at 0.5 ms–1 and 10 capital omega resistor is held at rest    

The correct answer is: Induced current equals fraction numerator 1 over denominator 150 end fraction Adirected anti-clockwise if 5 capital omega resistor is pulled to the left at 0.5 ms–1 and 10 capital omega resistor is held at rest


    When 5 capital omega resistor is pulled left at 0.5 m/sec induced emf., in the said resistor = e equals v B l equals 0.5 cross times 2 cross times 0.1 equals 0.1 V
    Resistor 10 capital omega is at rest so induced emf in it left parenthesis e equals v B l right parenthesis be zero.
    Now net emf.,
    in the circuit equals 0.1 V
    and equivalent
    resistance of the circuit
    R = 15 W
    Hence current i equals fraction numerator 0.1 over denominator 15 end fraction a m p equals fraction numerator 1 over denominator 150 end fraction a m p
    And its direction will be anti-clockwise (according to Lenz’s law)

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