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Question

An equilateral triangular loop having a resistance R and length of each side l is placed in a magnetic field which is varying at fraction numerator d B over denominator d t end fraction equals 1 T divided by s. The induced current in the loop will be

  1. fraction numerator square root of 3 over denominator 4 end fraction fraction numerator l to the power of 2 end exponent over denominator R end fraction    
  2. fraction numerator 4 over denominator square root of 3 end fraction fraction numerator l to the power of 2 end exponent over denominator R end fraction    
  3. fraction numerator square root of 3 over denominator 4 end fraction fraction numerator R over denominator l to the power of 2 end exponent end fraction    
  4. fraction numerator 4 over denominator square root of 3 end fraction fraction numerator R over denominator l to the power of 2 end exponent end fraction    

The correct answer is: fraction numerator square root of 3 over denominator 4 end fraction fraction numerator l to the power of 2 end exponent over denominator R end fraction


    phi equals fraction numerator square root of 3 over denominator 4 end fraction l to the power of 2 end exponent B
    epsilon equals open vertical bar fraction numerator d phi over denominator d t end fraction close vertical bar equals fraction numerator square root of 3 over denominator 4 end fraction l to the power of 2 end exponent fraction numerator d B over denominator d t end fraction
    i equals fraction numerator epsilon over denominator R end fraction equals fraction numerator square root of 3 over denominator 4 end fraction fraction numerator l to the power of 2 end exponent over denominator R end fraction

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