Now we shall estimate the flux linkages of the conductor due to the external flux. For this we will consider the flux linkages of an isolated conductor due to that portion of the external flux which lies between two points distant and meters from centre of conductor P

_{1 }and P_{2 }are two such points as shown in the Fig. 1.Fig. 1 |

The conductor shown in the Fig. 1 carries current I. The flux paths are concentric circles around the conductor between P

_{1 }and P_{2}.
Consider a tubular element which is x meters from centre of conductor. The field intensity at this point is H

The flux density B

The flux dΦ in the tubular element is given by,

dΦ = B

The flux linkages dψ per meter equal to dΦ since flux external to the conductor links all the current in the conductor. The total flux linkage between P

Since the μ = μ

For Relatively permeability, μ

The inductance due to flux included between P

In the external flux is considered to be extended from the surface of conductor to infinity then total flux linkages is given by,

Overall flux linkages is given by

_{x}. The mmf around the element isThe flux density B

_{x }at this point is given byThe flux dΦ in the tubular element is given by,

dΦ = B

_{x }x dx x 1m (Axial length is considered as 1m)The flux linkages dψ per meter equal to dΦ since flux external to the conductor links all the current in the conductor. The total flux linkage between P

_{1 }and P_{2 }are obtained by integrating dψ from D_{1 }to D_{2 }Since the μ = μ

_{o}μ_{r}For Relatively permeability, μ

_{r }= 1The inductance due to flux included between P

_{1 }and P_{2 }only is,Overall flux linkages is given by

Very elaborated explanation. Very good!!

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