Physics-
General
Easy

Question

A rectangular loop has a sliding connector P Q of length l and resistance R blank capital omega and it is moving with a speed v as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents I subscript 1 end subscript comma I subscript 2 end subscript a n d blank I are

  1. I subscript 1 end subscript equals negative I subscript 2 end subscript equals fraction numerator B l v over denominator R end fraction comma blank I equals fraction numerator 2 B l v over denominator R end fraction  
  2. I subscript 1 end subscript equals I subscript 2 end subscript equals fraction numerator B l v over denominator 3 R end fraction comma I equals fraction numerator 2 B l v over denominator 3 R end fraction  
  3. I subscript 1 end subscript equals I subscript 2 end subscript equals I equals fraction numerator B l v over denominator R end fraction  
  4. I subscript 1 end subscript equals I subscript 2 end subscript equals fraction numerator B l v over denominator 6 R end fraction comma I equals fraction numerator B l v over denominator 3 R end fraction  

The correct answer is: I subscript 1 end subscript equals I subscript 2 end subscript equals fraction numerator B l v over denominator 3 R end fraction comma I equals fraction numerator 2 B l v over denominator 3 R end fraction


    A moving conductor is equivalent to battery of emf
    equals v B l (motion emf)
    Equivalent circuit

    I equals I subscript 2 end subscript plus I subscript 2 end subscript
    Applying Kirchhoff’s law
    I subscript 1 end subscript R plus I R minus v B l equals 0 blank horizontal ellipsis left parenthesis i right parenthesis
    I subscript 2 end subscript R plus I R minus v B l equals 0 …(ii)
    Adding Eqs. (i) and (ii), we get
    blank 2 I R plus I R equals 2 v B l
    blank I equals fraction numerator 2 v B l over denominator 3 R end fraction
    I subscript 1 end subscript equals I subscript 2 end subscript equals fraction numerator v B l over denominator 3 R end fraction

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