Physics-
General
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Question

There exists a uniform but time varying magnetic field B = a + bt normal to plane of paper in a cylindrical region as shown. A rectangular conducting loop is placed as shown. Induced emf in branches AB and BC are

  1. pi R to the power of 2 end exponent b divided by 20    
  2. 2 R to the power of 2 end exponent b comma 0    
  3. 0 comma pi R to the power of 2 end exponent b divided by 8    
  4. 0 comma pi R to the power of 2 end exponent b divided by 4    

The correct answer is: 0 comma pi R to the power of 2 end exponent b divided by 8

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In given figure, a wire loop has been bent so that it has three segments: segment ab (a quarter circle), bc (a square corner), and ca (straight). Here are three choices for a magnetic field through the loop:

text 1)  end text stack B with rightwards arrow on top subscript 1 end subscript equals 3 stack i with hat on top plus 7 stack j with hat on top minus 5 t stack k with hat on top comma text  2)  end text stack B with rightwards arrow on top subscript 2 end subscript equals 5 t stack i with hat on top minus 4 stack j with hat on top minus 15 stack k with hat on top comma text  3)  end text stack B with rightwards arrow on top subscript 3 end subscript equals 2 stack i with hat on top minus 5 stack t with hat on top minus 12 stack k with hat on top
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In given figure, a wire loop has been bent so that it has three segments: segment ab (a quarter circle), bc (a square corner), and ca (straight). Here are three choices for a magnetic field through the loop:

text 1)  end text stack B with rightwards arrow on top subscript 1 end subscript equals 3 stack i with hat on top plus 7 stack j with hat on top minus 5 t stack k with hat on top comma text  2)  end text stack B with rightwards arrow on top subscript 2 end subscript equals 5 t stack i with hat on top minus 4 stack j with hat on top minus 15 stack k with hat on top comma text  3)  end text stack B with rightwards arrow on top subscript 3 end subscript equals 2 stack i with hat on top minus 5 stack t with hat on top minus 12 stack k with hat on top
Where stack B with rightwards arrow on top is in milliteslas and t is in seconds. If the induced current in the loop due to stack B with rightwards arrow on top subscript 1 end subscript comma stack B with rightwards arrow on top subscript 2 end subscript text  and  end text stack B with rightwards arrow on top subscript 3 end subscript are i subscript 1 end subscript comma i subscript 2 end subscript text  and  end text i subscript 3 end subscript respectively then

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