Physics-
General
Easy

Question

Two long parallel conductors carry currents in opposite directions as shown. One conductor carries a current of 10 A and the distance between the wires is d=10cm  Current I is adjusted, so that the magnetic field at P is zero. P is at a distance of 5 cm to the right of the 10 A current. Value of I is

  1. 40 A    
  2. 30 A    
  3. 20 A    
  4. 10 A    

The correct answer is: 30 A


    From Biot-Savart’s law the magnetic field open parentheses B close parentheses due to a conductor carrying current I comma at a distance r subscript 1 end subscript is
    B subscript 1 end subscript equals fraction numerator mu subscript 0 end subscript I subscript 1 end subscript over denominator 2 pi r subscript 1 end subscript end fraction
    Magnetic field at P due to current in second conductor is
    B subscript 2 end subscript equals fraction numerator mu subscript 0 end subscript I subscript 2 end subscript over denominator 2 pi open parentheses r subscript 1 end subscript plus d close parentheses end fraction
    From Fleming’s right hands rule the fields at P are directed opposite.
    therefore R e s u l t a n t s comma blank f i e l d blank B subscript 1 end subscript equals B subscript 2 end subscript
    therefore blank fraction numerator mu subscript 0 end subscript I subscript 1 end subscript over denominator 2 pi r subscript 1 end subscript end fraction equals blank fraction numerator mu subscript 0 end subscript I subscript 2 end subscript over denominator 2 pi open parentheses r subscript 1 end subscript plus d close parentheses end fraction
    Given, I subscript 1 end subscript equals 10 blank A comma blank r subscript 1 end subscript equals 5 comma blank r subscript 1 end subscript plus d equals 5 plus 10 equals 15 blank c m
    therefore blank I subscript 2 end subscript equals fraction numerator I subscript 1 end subscript over denominator r subscript 1 end subscript end fraction blank cross times open parentheses r subscript 1 end subscript plus d close parentheses
    I subscript 2 end subscript equals fraction numerator 10 over denominator 5 end fraction cross times 15 equals 30 blank A

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