Force on a Current-Carrying Wire

Look inside a loudspeaker or an electric motor and you’ll find the same quiet trick doing all the work: a wire carrying a current, sitting inside a magnetic field, gets pushed. Not a nudge you have to imagine — a real, measurable force you can calculate and point in a direction. This page shows you exactly how big that push is and which way it goes.

Why a Current-Carrying Wire Gets Pushed

On the last page we saw that a current makes its own magnetic field, looping in circles around the wire. Now put that wire inside another magnetic field — say between the poles of a magnet. The wire’s own field and the external field can’t sit politely on top of each other: they combine, bunching up on one side of the wire and thinning out on the other. That lopsided field is what pushes the wire sideways, and we call it the motor effect.

You can watch it in a moment: rest a loose copper rod across two rails inside a magnet’s field and connect it to a battery. The instant current flows, the rod rolls — jumping in the direction of the force. Switch the current off and it stops. That little jump is the same physics that spins every electric motor.

How Big Is the Force? F = BIL sin θ

The strength of the push is set by one tidy equation. It gathers together everything that could reasonably matter — how strong the field is, how much current flows, how much wire is in the field, and how the wire is angled.

Reading it symbol by symbol: F is the force on the wire (N); B is the flux density of the applied field (T); I is the current in the wire (A); L is the length of wire (m); and θ is the angle between the wire and the field. So the force grows if you turn up any of three things — a stronger field, a bigger current, or a longer wire in the field.

One detail examiners love: L is only the length of wire that is actually inside the field. If a 30 cm wire pokes through a magnet’s gap but just 4 cm of it sits between the poles, then L = 0.04 m, not 0.30 m. The rest of the wire is out in the open, feeling nothing.

The Angle Does the Steering

That sin θ on the end is doing something important: it measures how squarely the wire cuts across the field. Line the wire up at right angles to the field and it slices straight through the lines — maximum push. Lay it along the lines instead and it never crosses them — no push at all.

Which Way Does It Push? Fleming’s Left-Hand Rule

Now for the direction. The force, the field and the current are always mutually perpendicular — pick any two and the third sticks out at a right angle to both. To untangle which way is which, we use Fleming’s left-hand rule. Hold out your left hand with the thumb, first finger and second finger all at right angles, and each one names a quantity:

• thuMb → Motion (the force F)
• First finger → Field (the applied field B, pointing N → S)
• seCond finger → Current (the conventional current I, from + to −)

The letters do the remembering for you: M–F–C hides inside thuMb, First, seCond.

Those dots and crosses come up constantly, so pin the picture down: think of an arrow in flight. Coming straight at you (out of the page) you’d see only its sharp tip — a dot. Flying away from you (into the page) you’d see only the crossed feathers at its tail — a cross.