please explain elaborately

By Ampere's law , magnetic field induction B  near current carrying wire is given as

 

  .........................(1)

where μ_o is permeability of free space , r is radial distance from central axis of wire and

I_enc is enclosed current within the circle of radius drawn with axis of wire as centre.

 

Let I be the current passing through wire of circular cross section radius R .

 

At a point , which is at distance r from centre of wire crosssection , within the wire ( r < R ),

magnetic field induction B(r) is obtained from eqn.(1) by substituting enclosed current.

 

I_enc = crosssection area of radius r × current density =  ( π r² ) × [  I / ( π R² ) ] = I × ( r² / R² )

 

where I is the current passing through wire.

 

Magnetic field induction B(r)  , when r < R is given as

 

...................................(2)

 

 

At a radial distance r = R , i.e., when the point is on the surface of wire ,

Magnetic field induction B(r) is obtained from eqn.(2) by substituting r = R

 

 ....................... (3)

At a radial distance r > R , i.e., when the point is outside the wire , enclosed current is simply I

 

Hence we get magnetic field induction B from eqn.(1) as

 

Plot of the magnetic field induction as a finction of radial distance is shown in figure.