Question

the magnetic induction at a distance r from a long straight conducting wire current I ampere is..??

Answer 1

Consider a straight infinitely long wire carrying a steady current I. The line AP is perpendicular to the wire, and is of length R.  From the Biot-Savart law, the magnetic field dB due to a small element dl of the wire near the point O at a distance |r| = r from P (OP=r) is 

                                                                µo I        

dl x r

                                                  dB =  -------    ---------

                                                   4 p

 

      r3

Since the current element dl and the vector r make an angle q with each other, the product dl*r has a magnitude dlr sin q.  It is directed perpendicular to both dl and r.  This is the direction perpendicular to the plane of the paper and going into it, as is clear from the right handed corkscrew rule (link) (direction of advance of a right handed corkscrew turning from dl to r).  

        µo      I dl sin  q

dB =   ---- -------k

   4 p

 

     r2

    The magnetic field at a point P due to a infinite (very long) straight wire carrying a current I is proportional to I, and is inversely proportional to the perpendicular distance R of the point from the wire.  The integral J has a value of 2, so that

 

                                               µo           I

                                       B =  ----  ---- k    tesla (Wb/m2)

                                               2 p

 

      R

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