Biot-Savart Law

Magnetic field from a long straight wire

An infinitely long conductor with current results in a magnetic field strength at a perpendicular distance .¹

While this scenario is impossible for obvious reasons, it approximates the -field short distances from a long section of straight wire in a large circuit. Since is always in the direction of current², the right hand rule shows that any point with a positive in the above setup will experience out of the page (while the opposite is true for negative ). Using these observations, solving the Biot-Savart Law for this setup gives

where the direction of the -field can be determined by a right hand rule: point the thumb in the direction of current and the curl of the fingers corresponds to the direction of the -field.

Combining this with Magnetic force on a wire, we can derive the Force between two straight current carrying wires.

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