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in calculating inductance of a single current carrying conductor how flux linkage is calculated?why flux is multiplied by a factor (X^2)/(r^2) to get flux linkage. see the following images:

see the red marked line

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  • \$\begingroup\$ I believe this is calculating the flux linkages internal to the conductor as a means of ascertaining total flux inside the conductor. Because current density varies in the conductor (with distance from the centre) it's a means of getting the total flux. I may be wrong - if you can link to an online document it might be easier to read. \$\endgroup\$
    – Andy aka
    Nov 13 '15 at 19:39
  • \$\begingroup\$ EM equations are based on vector calculus. This is a simplified flux integral for a share carrier with cylindrical symmetry. The scalLing factor is the transformation from dxdydz to a dphi basis \$\endgroup\$
    – crasic
    Nov 13 '15 at 21:44
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dPhi is written as the flux through a cylindrical shell (dx) for a current I.

However, in this case, flux linkage is only part of the total flux derived from I, that is, the flux that derives from the part of the current that goes through a radial section of radius x < r.

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