The force on a current.

Step 1 of 4

A push sideways

A current is charges on the move, and in the last Lesson you saw that it makes a magnetic field of its own. So a magnet pushes on a wire carrying a current, as it pushes on another magnet. But this force is surprising: it points neither at the poles nor along the wire. It is at right angles to both the current and the field.

The direction comes from the right-hand rule: point the fingers of your right hand along the current, curl them towards the field, and your thumb shows the force. Reverse the current or the field, and the force reverses.

Show the forces is On: the field lines run between the poles, and the green arrows show the push on the coil’s two sides.

Step 2 of 4

How hard

A straight wire of length $L$⁠ at right angles to a field $B$⁠ and carrying a current $I$⁠ feels a force

$F = B I L$⁠

In the motor’s coil each long side is $N$⁠ such wires side by side, so each side is pushed with $F = N B I L$⁠. The current and the field are fixed now. Work out the force on one side.

Step 3 of 4

Twice as hard

The force is in proportion to the current and to the field, so the same force can be reached in different ways.

Step 4 of 4

From a push to a turn

The coil’s two long sides carry the current opposite ways, so they are pushed opposite ways: one up and one down, on either side of the axle. Such a pair turns the coil. The two short sides lie almost along the field when the coil is level, and a current along the field feels no force at all: the force is $B I L$⁠ only when the current is at right angles to the field, and it shrinks as the angle between them closes.

Every half turn, the commutator reverses the current in the coil, so the pushes keep turning it the same way.

Try it: raise Current or Magnetic field, and watch the coil settle to a faster spin.

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