How this calculator works
Ampere law around a circular path gives a magnetic field inversely proportional to radius for a long straight wire. Positive current defines the positive azimuthal direction through the right-hand rule. This model assumes a uniform linear surrounding medium and a point outside the conductor, with wire ends and the return conductor far away. The vacuum permeability is the CODATA 2022 measured value, not an exact 4 pi times 1e-7.
Formula
Bphi = mu0 mur I/(2 pi r). I = 2 pi r Bphi/(mu0 mur), r = mu0 mur I/(2 pi Bphi).
Worked example
At 1 m from a 10 A wire in vacuum, the field is about 2 microteslas. Reversing current to -20 A, using r = 2 m and relative permeability 2 gives about -4 microteslas.
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Frequently asked questions
How long must the wire be?
The distance to either end and the return path should be much larger than the radial distance for the infinite-wire approximation to work well.
Can I calculate the field inside the wire?
No. Inside a finite-radius conductor, the enclosed-current distribution must be modelled.
Why use a signed field?
It records the azimuthal direction relative to the right-hand rule for positive current.