Physics-
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Question

A highly conducting ring of radius R is perpendicular to and concentric with the axis of a long solenoid as shown in fig. The ring has a narrow gap of width d in its circumference. The solenoid has cross sectional area A and a uniform internal field of magnitude B subscript 0 end subscript. Now beginning at t equals 0, the solenoid current is steadily increased so that the field magnitude at any time t is given by B open parentheses t close parentheses equals B subscript 0 end subscript plus alpha t where a greater than 0. Assuming that no charge can flow across the gap, the end of ring which has excess of positive charge and the magnitude of induced e.m.f. in the ring are respectively

  1. X comma blank A alpha  
  2. X comma blank pi R to the power of 2 end exponent alpha  
  3. Y comma blank pi A to the power of 2 end exponent alpha  
  4. Y comma blank pi R to the power of 2 end exponent alpha  

The correct answer is: X comma blank A alpha


    Since the current is increasing, so inward magnetic flux linked with the ring also increases (as viewed from left side). Hence induced current in the ring is anticlockwise, so end x will be positive
    Induced emfopen vertical bar e close vertical bar equals A fraction numerator d B over denominator d t end fraction equals A fraction numerator d over denominator d t end fraction open parentheses B subscript o end subscript plus alpha t close parentheses rightwards double arrow open vertical bar e close vertical bar equals A alpha

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