Physics-
General
Easy

Question

Curves in the graph shown give, as functions of radial distance r, the magnitude B of the magnetic field inside and outside four long wires a, b, c and d, carrying currents that are uniformly distributed across the cross sections of the wires. Overlapping portions of the plots are indicated by double labels.

Which wire has the greatest radius ?

  1. a    
  2. b    
  3. c    
  4. d    

The correct answer is: c


    Inside the cylinder

    table row cell B 2 pi r equals mu subscript 0 end subscript comma fraction numerator I over denominator pi R to the power of 2 end exponent end fraction pi r to the power of 2 end exponent end cell row cell B equals fraction numerator mu subscript 0 end subscript I over denominator 2 pi R to the power of 2 end exponent end fraction times r end cell row cell text end text text o end text text u end text text t end text text s end text text i end text text d end text text e end text text end text text t end text text h end text text e end text text end text text c end text text y end text text l end text text i end text text n end text text d end text text e end text text r end text text end text end cell row cell B.2 pi equals mu subscript I end subscript 1 end cell row cell B equals fraction numerator mu subscript 0 end subscript I over denominator 2 pi r end fraction end cell end table
    Inside cylinder B proportional tor and outside B proportional to fraction numerator 1 over denominator r end fraction
    So from surface nature of mag field changes. Hence it is clear from the graph that wire 'c' has greatest radius

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