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When dealing with the magnetic field generated by a current-carrying wire, the formula for the magnetic flux density is B = μi/2π·d, but what if the point is located on the wire it self?

In this case d = 0 and B = infinity, or B will be 0 as the flux lines do not intersect this point and produce a magnetic field. In this question I neglect B2 generated by i2 and set it to 0.

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  • \$\begingroup\$ What is the relevance of the diagram? \$\endgroup\$
    – Andy aka
    Mar 19 at 8:56

2 Answers 2

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Assuming a uniform current density over the wire cross section.

If \$d<r\$ the radius of the wire, then the contributing current within \$d\$ decreases. as \$d->0\$ the contributing current goes to zero. Integrating over the currents outside \$d\$ will produce a zero result.

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When the observation point is far from the wire, you can treat it as a single strand of current and use the formula.

When you're fairly close to the wire then you need to treat it as many strands of current arranged throughout the wire area, and add up or integrate the magnetic field contribution dB from each small current dI, in its area dA, at its radius from the observation point.

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