Physics-
General
Easy

Question

In the figure shown, the magnetic field induction at the point O will be

  1. fraction numerator mu subscript 0 end subscript i over denominator 2 pi r end fraction    
  2. open parentheses fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction close parentheses open parentheses fraction numerator i over denominator r end fraction close parentheses open parentheses pi plus 2 close parentheses    
  3. open parentheses fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction close parentheses open parentheses fraction numerator i over denominator r end fraction close parentheses open parentheses pi plus 1 close parentheses    
  4. fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator i over denominator r end fraction open parentheses pi minus 2 close parentheses    

The correct answer is: open parentheses fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction close parentheses open parentheses fraction numerator i over denominator r end fraction close parentheses open parentheses pi plus 2 close parentheses


    Field due to a straight wire of infinite length is fraction numerator mu subscript 0 end subscript i over denominator 4 pi r end fraction if the point is on a line perpendicular to its length while at the centre of a semicircular coil is fraction numerator mu subscript 0 end subscript pi i over denominator 4 pi r end fraction.

    therefore B equals B subscript a end subscript plus B subscript b end subscript plus B subscript c end subscript
    equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator i over denominator r end fraction plus blank fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator pi i over denominator r end fraction plus fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator i over denominator r end fraction
    equals fraction numerator mu subscript 0 end subscript over denominator 4 pi end fraction fraction numerator i over denominator r end fraction open parentheses pi plus 2 close parentheses out of the page

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