Magnetic field action and motor

A current-carrying wire deflects between magnetic poles. How can force on a straight wire rotate a loop, even when the forces on it sum to zero?

Switch on current in a wire across a magnet's field. Moving charges experience magnetic force and transfer its effect to the wire through interactions with the material. A force arises perpendicular to current and field. Switch current off and this effect disappears even though the magnet remains. Distinguish this force on current from a magnet attracting iron: the wire need not be iron.

Use the left-hand rule to check force direction. Hold the palm so B enters it, with four fingers along conventional current. The thumb held out at 90° indicates force. Reverse only current and force reverses; reverse only field and it also reverses; reverse both and force keeps its direction. Use conventional current, not the oppositely directed electron motion.

What sets the strength of the deflection? For a wire across the field, a stronger field, more current or a longer section in the field each increases the force. Magnetic flux density B characterises the field and is measured in teslas, T. Active length l, in metres, includes only wire inside the field considered; F is in N. Supply leads outside the field are not part of this length.

For a straight section perpendicular to a uniform field, these relationships combine as F = BIl. Doubling B, I or active length separately doubles F; at zero current F is zero. With B in T, I in A and l in m, the result is N. Rotating the wire changes the result: along the field lines this force vanishes. Do not use F = BIl for an arbitrary tilted section and ignore perpendicularity.

Bend the wire into a loop. Opposite sides carry opposite currents, so magnetic forces are opposite too. They may seem to cancel completely. But they act at different places and can create torque, like turning a steering wheel with two hands. Their sum can be zero while a turning effect remains. Its magnitude depends on loop orientation and the forces' lever arms.

With current direction unchanged, a loop tends towards a particular orientation rather than rotating endlessly one way. In a simple commutator motor, current reverses every half-turn so the forces support rotation again after passing that orientation. Inertia and motor design help it pass through. Electrical energy becomes mechanical work, with some lost to heating and other processes.

Why does a compass work far from a laboratory magnet? Earth's magnetic field aligns it. Its north end usually points roughly towards geographic north. External field lines enter Earth there, so this region acts with magnetic south polarity and attracts the needle's north end. Magnetic and geographic poles do not coincide; a compass is therefore not an infallible guide to geographic north.

Bring a magnet or current-carrying wire near a compass and the needle can deflect markedly. It responds to the local combined field, not specifically to Earth alone. Iron objects can also change this field. Test a compass away from unwanted magnetic influences. If it turns unexpectedly, first look for a nearby field change, not a shift of the geographic pole.

In a uniform field B = 0,2 Тл, a 0.1 m section carrying 3 A lies perpendicular to the field lines. Find the force magnitude.

Find force magnitude on the 0.1 m active section. The field is uniform and the wire is perpendicular, so F = BIl applies.

F = 0,2·3·0,1 = 0,06 Н. Doubling active length at the same current and field would double force.

This product does not determine force direction. The left-hand rule needs field and current directions; the problem asks only for magnitude.

The force magnitude is 0.06 N. It acts on the specified wire section, not the full circuit length.

F = BIl describes a straight section across a uniform field; current and field set the direction.

Separated opposite forces can rotate a loop even with zero net force.

A motor maintains rotation by switching current; a compass follows the local combined field.

Next we reverse cause and effect: moving a magnet can produce a voltage.