please explain elaborately

Asked by nelsonsanabam46 | 13th Nov, 2020, 06:29: PM

Expert Answer:

By Ampere's law , magnetic field induction B  near current carrying wire is given as
 
begin mathsize 14px style B left parenthesis r right parenthesis space equals space fraction numerator mu subscript o over denominator 2 pi r end fraction space I subscript e n c end subscript end style  .........................(1)
where μo is permeability of free space , r is radial distance from central axis of wire and
Ienc 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.
 
Ienc = 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
 
begin mathsize 14px style B left parenthesis r right parenthesis space equals space fraction numerator mu subscript o over denominator 2 pi r end fraction cross times I space r squared over R squared space equals space fraction numerator mu subscript o space I over denominator 2 pi end fraction cross times open parentheses r over R squared close parentheses end style...................................(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
 
begin mathsize 14px style B left parenthesis r right parenthesis space equals space fraction numerator mu subscript o over denominator 2 pi r end fraction cross times I space r squared over R squared space equals space fraction numerator mu subscript o space I over denominator 2 pi end fraction cross times open parentheses 1 over R close parentheses end style ....................... (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
 
begin mathsize 14px style B left parenthesis r right parenthesis space equals space fraction numerator mu subscript o over denominator 2 pi r end fraction space I end style
Plot of the magnetic field induction as a finction of radial distance is shown in figure.

Answered by Thiyagarajan K | 14th Nov, 2020, 10:29: AM

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