The relative direction between a magnetic field and a current-carrying wire results in the greatest force is perpendicular to each other. This is based on the Lorentz force equation on a current-carrying wire.
The Lorentz force is the force resulted due to the current in a magnetic field. On a current-carrying wire, the Lorentz force can be expressed as
F = B I l sin θ
Where
If we wish the greatest force, then sin θ value should be 1.
sin θ = 1
θ = 90°
The angle between a magnetic field and a current-carrying wire for getting the greatest force is 90°. it means that the direction of a current-carrying wire is perpendicular to a magnetic field.
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