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A wire cd of length l and mass m is sliding without friction on conducting rails ax and by as shown. The vertical rails are connected to each other with a resistance R between a and b. A uniform magnetic field B is applied perpendicular to the plane abcd such that cd moves with a constant velocity of

  1. fraction numerator m g R over denominator B l end fraction    
  2. fraction numerator m g R over denominator B to the power of 2 end exponent l to the power of 2 end exponent end fraction    
  3. fraction numerator m g R over denominator B to the power of 3 end exponent l to the power of 3 end exponent end fraction    
  4. fraction numerator m g R over denominator B to the power of 2 end exponent l end fraction    

The correct answer is: fraction numerator m g R over denominator B to the power of 2 end exponent l to the power of 2 end exponent end fraction


    Due to magnetic field, wire will experience an upward force F equals B i l equals B   open parentheses fraction numerator B v l over denominator R end fraction close parentheses   l rightwards double arrow F equals fraction numerator B to the power of 2 end exponent v l to the power of 2 end exponent over denominator R end fraction
    If wire slides down with constant velocity then
    F equals m g rightwards double arrow fraction numerator B to the power of 2 end exponent v l to the power of 2 end exponent over denominator R end fraction equals m g rightwards double arrow v equals fraction numerator m g R over denominator B to the power of 2 end exponent l to the power of 2 end exponent end fraction

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