Write the relation for the magnetic field induction at a point due to a linear conductor carrying current and hence deduce the relation for the magnetic field induction at a point due to a very long linear conductor carrying current.

Explanation

Magnetic field induction at a point P in space at a perpendicular distance a from a linear conductor carrying current I is
`B=(mu_0)/(4pi)i/a(sin phi_1+sin phi_2)`
where `phi_1` and `phi_2` are the angles subtended by the lines joining the ends of linear conductor with point P and perpendicular drawn on the conductor from point P.
In case of infinitely long conductor,
`phi_1=pi/2=phi_2`
`:. B=(mu_0)/(4pi)i/a(sinpi/2+sinpi/2)=(mu_0)/(4pi)(2i)/(a)`