Motor Effect

Causes of the motor effect

The basis of the motor effect is the fact that an electric current flowing through a wire produces a magnetic field.

Recall that a current-carrying wire has a cylindrical magnetic field around it (as explained in the article 'Electric Fields of Electric Currents'). If you place the current-carrying wire inside an external magnetic field, the cylindrical magnetic field accompanying the current will interact with the external magnetic field. It is this interaction that produces a force on the wire: it is just like the force between two bar magnets being caused by their magnetic fields interacting with each other!

Motor Effect: Direction of the force

You can use Fleming's left-hand rule to figure out the direction of the force in the motor effect if you know the direction of the current and the external magnetic field involved. Fleming's left-hand rule states that, if you hold your left hand as in the image below, your thumb indicates the direction of the force, your index finger indicates the direction of the external magnetic field, and your middle finger indicates the direction of the current. We see that the direction of the force$F$is always perpendicular to the plane in which both the magnetic field$B$and the current$I$lie.

Formula of the motor effect

Not only do we want to know the direction of the force on the wire, but we also want to know how big this force is. If the wire is perpendicular to the magnetic field lines, the motor effect formula relates the current through the wire, the length of the wire that is in the magnetic field, and the magnetic field strength to the force that the wire experiences.

$\mathrm{force}\mathrm{on}\mathrm{the}\mathrm{wire}=\mathrm{magnetic}\mathrm{field}\mathrm{strength}\times \mathrm{current}\mathrm{through}\mathrm{wire}\times \mathrm{length}\mathrm{of}\mathrm{wire}\mathrm{in}\mathrm{magnetic}\mathrm{field}$.

Written using symbols, we get the equation

$F=BI\mathcal{l}$,

where

• $F$is the force on the wire in$\mathrm{N}$(newtons),
• $B$is the magnetic field strength in$\mathrm{T}$(teslas),
• $I$is the current through the wire in$\mathrm{A}$(amperes),
• $\mathcal{l}$is the length of the wire in$\mathrm{m}$(metres) that is in the external magnetic field.

This is a logical formula, because the stronger the magnetic field, or the higher the electric current, or the more of the wire is in the magnetic field, the bigger the force on the wire.

Diagram of the motor effect

Below is a diagram of the motor effect, where the horseshoe magnet's north pole is red and its south pole is green. The diagram shows the direction of the force as a result of the direction of the magnetic field and the current.

Diagram of the motor effect for a currentthrough the wire, a magnetic field strengthin the wire, and a forceon the wire, Wikimedia Commons CC BY-SA 4.0.

Motor effect experiments

There are countless applications of the motor effect in everyday electromechanical devices. Below are some examples of simple experiments demonstrating the motor effect.