The Motor Effect

An electric fan, a cordless drill, the window motors in a car, the wheels of an electric train — all of them spin because of one neat trick of physics. Send a current down a wire, lay that wire between the poles of a magnet, and the wire suddenly jumps. Nothing touches it; the wire just leaps sideways, all on its own, the instant the current flows.

This kick is the motor effect: a current-carrying wire placed in a magnetic field feels a force. It is the seed of every electric motor ever built. In this page we'll find out why the wire moves, how big the push is, and which way it points.

Why does the wire move? Two fields, one squeeze

A current is just moving charge, and every current makes its own magnetic field — little circles wrapped around the wire (you met this with electromagnets). So now there are two magnetic fields in the same place: the straight field of the magnet running from N to S, and the circular field of the wire looping around it.

On one side of the wire the two fields point the same way and reinforce, packing the field lines tightly. On the other side they point opposite ways and cancel, thinning the lines out. Field lines behave a bit like stretched elastic that hates being crowded, so the wire is squeezed out of the crowded side towards the empty side — and off it shoots. Some people call this the catapult field, because the bunched-up lines fling the wire away like a catapult.

How big is the push? F = B\,I\,L

Three things make the force bigger: a stronger magnet, a bigger current, and a longer piece of wire sitting in the field. Put them together and you get one of the most useful equations in electromagnetism.

When a wire at right angles to a magnetic field carries a current, the force on it is

F = B\,I\,L

F — the force on the wire, in newtons (N);
B — the magnetic flux density (how strong the field is), in tesla (T);
I — the current in the wire, in amperes (A);
L — the length of wire inside the field, in metres (m).

This size is for a wire at 90^\circ to the field. Turn the wire to lie along the field and the force falls all the way to zero.

That last point is worth holding on to: the motor effect is greatest when the wire is at 90^\circ (perpendicular) to the field, and zero when the wire lies parallel to it. In between, only the part of the field that crosses the wire at right angles does any pushing.

Worked examples

Example 1 — find the force. A straight wire of length L = 0.2\ \text{m} sits at right angles in a field of B = 0.4\ \text{T} and carries a current of I = 3\ \text{A}. What force does it feel?

F = B\,I\,L = 0.4 \times 3 \times 0.2 = 0.24\ \text{N}.

A quarter of a newton — small, but multiply it up over the many turns of a real coil and it is more than enough to spin a motor.

Example 2 — rearrange for the current. A wire of length L = 0.3\ \text{m} lies at 90^\circ in a field of B = 0.5\ \text{T} and is measured to feel a force of F = 0.6\ \text{N}. What current is flowing? Rearrange F = B\,I\,L for I:

I = \frac{F}{B\,L} = \frac{0.6}{0.5 \times 0.3} = \frac{0.6}{0.15} = 4\ \text{A}.

The same triangle trick works for B = \dfrac{F}{I\,L} or L = \dfrac{F}{B\,I} — cover the one you want and read off the rest.

Which way does it push? Fleming's left-hand rule

The force, the field and the current are all at right angles to each other — three directions, each one perpendicular to the other two. To untangle them, hold up your left hand with your thumb, first finger and second finger stuck out at 90^\circ to each other, like a corner of a box:

Thumb → Thrust (the Force / the way the wire moves);
First finger → Field (points from N to S);
seCond finger → Current (the direction the current flows).

Line your First finger up with the field and your seCond finger along the current, and your thumb automatically points the way the wire is thrust. It takes a little wrist-twisting the first few times — that's normal.

Now flip things around. Reverse the current (send it the other way) and the thumb turns to point the opposite way: the force reverses. Reverse the field (swap the magnet's poles) and, again, the force reverses. This is exactly how you steer a motor.

Three traps that catch people out with the motor effect:

Angle matters. The force is biggest when the wire is at 90^\circ to the field and drops to zero when the wire lies parallel to it. A wire pointing the same way as the field feels no push at all.
Use your LEFT hand for the motor effect. Left hand = motor (current in → movement out). The right hand is for the generator effect (movement in → current out) — a different rule for a different job. Mix them up and every direction comes out backwards.
Reversing BOTH leaves it unchanged. Reverse the current or the field and the force flips. Reverse both at once and the two flips cancel — the force points exactly the same way as before.

See it for yourself

Below, a wire (the circle) runs between the poles of a magnet — the field points from N on the left to S on the right, and the current runs straight through the wire, out of the screen towards you (shown as a dot ●) or into the screen away from you (shown as a cross ✕). The green arrow is the force from F = B\,I\,L.

Turn up the current or the field and watch the force arrow grow. Switch the current direction from Normal to Reversed and watch the whole arrow flip over — just as Fleming's left-hand rule promises.

From a kicking wire to a spinning motor

A single wire only jumps once and stops. To get continuous spinning we bend the wire into a coil (a loop) and mount it so it can turn between the magnet's poles. Now the two sides of the loop carry current in opposite directions, so by Fleming's left-hand rule one side is pushed up and the other is pushed down. That pair of opposite forces spins the coil — a turning effect, or moment.

But there's a snag. After half a turn the two sides have swapped places, so the up-push and down-push would now fight the spin and the coil would just wobble to a stop. The fix is a clever switch called the split-ring commutator: a ring cut into two halves that the coil is wired to. Every half-turn the gap in the ring slides past the contacts (the brushes) and swaps the current in the coil the other way round. Because the current flips at exactly the right moment, the forces keep pushing the coil the same way round — so it spins on and on. That is a simple d.c. motor.

To make the motor stronger you use the same three levers as F = B\,I\,L: a bigger current, a stronger magnet, and more turns of wire in the coil (which is like having more length L in the field).

Once you know the trick you'll spot it everywhere. The motor effect spins the blades of a fan and a hairdryer, whirls the drum of a washing machine, drives the wheels of an electric car and a train, buzzes your phone on silent, and moves the read head of a hard drive.

And it doesn't have to spin. A loudspeaker is the motor effect turned into sound: a coil glued to the back of the paper cone sits in a magnet's field, and the wiggling music current makes the coil — and the cone — punch back and forth thousands of times a second, pushing the air into the sound you hear. Every speaker, earbud and headphone you own is really a tiny, very fast, back-and-forth motor.