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# Motor Effect Save Print Edit
Motor Effect
• Astrophysics • Atoms and Radioactivity • Electricity • Energy Physics • Engineering Physics • Fields in Physics • Force • Further Mechanics and Thermal Physics • Magnetism • Measurements • Mechanics and Materials • Medical Physics • Modern Physics • Nuclear Physics • Particle Model of Matter • Physical Quantities and Units • Physics of Motion • Radiation • Space Physics • Turning Points in Physics • Waves Physics Almost all household appliances have electric motors in them, including hair dryers, washers, and fans. But have you ever wondered how electric motors work? Specifically, how do they produce the force that they deliver, and why don't they make any noise? It is all based on the motor effect, an interaction between a current-carrying wire and a magnetic field. This interaction produces a force on the wire, and it is this force that we can use in all kinds of practical situations! Learn about the motor effect in this article.

## Definition of the motor effect

When a horseshoe magnet is placed around a current-carrying wire, the wire will deflect! Evidently, something is exerting a force on the wire in order to make it deflect. This force exists because of the interaction between the electricity in the wire with the magnetic field of the horseshoe magnet. The motor effect describes how electricity and magnets can work together to create a magnetic force. This magnetic force is the basis of all electric motors, hence the name 'motor effect'.

The motor effect is the phenomenon of a force being generated on a current-carrying wire in the presence of an external magnetic field.

## 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 is always perpendicular to the plane in which both the magnetic field and the current lie.

Practice using Fleming's left-hand rule until you get correct answers to questions regarding the direction of the quantities in the motor effect consistently. Fleming's left-hand rule shows the direction of the force on a conductor carrying a current in an external magnetic field, Wikimedia Commons CC BY-SA 4.0

If a current is running from south to north, and the magnetic field lines (from the magnetic field that the wire is in) run from west to east, then the force on the wire is downwards. Check this with Fleming's left-hand rule!

## 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. .

Written using symbols, we get the equation ,

where

• is the force on the wire in (newtons),
• is the magnetic field strength in (teslas),
• is the current through the wire in (amperes),
• is the length of the wire in (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.

If the wire is not perpendicular to the magnetic field, then we should add a term to the right-hand side of the equation - where is the angle between the wire and magnetic field, shown in the diagram above: .

This ensures that we only take the component of the current that is perpendicular to the magnetic field.

A wire carrying a current of with a length of is partially suspended in a magnetic field with a magnetic field strength of . The part of the wire that is in the magnetic field measures in length.

In this case, we only consider the section of wire that's in the magnetic field, so: , .

## Diagram of the motor effect

Below is a nice 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.

The simplest experiment you can do to demonstrate the motor effect is to get a horseshoe magnet and a wire that can carry a current. If you position the wire between the two poles of the horseshoe magnet, and drive a current through the wire, the motor effect will create a force on the wire, and the wire will deflect (if the force is big enough to overcome the weight and the friction of the wire).

Another experiment is one involving a battery, a small disc magnet, and some conducting wire. The setup is shown in the figure below: we place the magnet under the battery, and we bend and position the wire as shown.

• The magnetic field lines will go up and outwards from the magnet, so the magnetic field will be in opposite directions on both sides of the wire.
• The current will be from top to bottom (because the positive battery terminal is at the top), so the current will be downwards everywhere in the vertical parts of the wire.
• This causes the magnetic force generated on the wire to be opposite on either side, so the wire will start spinning around the battery. An experimental setup to demonstrate the motor effect, Wikimedia Commons CC BY-SA 4.0.
This experiment converts the chemical energy stored in the battery into kinetic energy stored in the wire using the motor effect. We now see that the motor effect is a good name because this experiment creates a rudimentary form of an electric motor!

## Motor Effect - Key takeaways

• The motor effect is the magnetic force on a current-carrying wire in a magnetic field.
• The motor effect is the result of the magnetic field of a current-carrying wire interacting with an external magnetic field.
• The direction of the force can be figured out using Fleming's left-hand rule.
• The formula of the motor effect tells you how big the force on a current-carrying wire perpendicular to a magnetic field is: .
• The motor effect equation shows that to increase the size of the force, we can; increase the strength of the magnetic field, pass a higher current through the wire, or use a longer length of wire in the field.
• Two simple experiments to demonstrate the motor effect are:
• Putting a current-carrying wire between the poles of a horseshoe magnet;
• Making a simple motor by setting up a battery with a magnet and wire attached as shown in the figure above.

The motor effect is the magnetic force on a current-carrying wire in a magnetic field.

The motor effect works through the magnetic force acting on the individual moving charged particles in the current-carrying wire.

The formula describing the size of the force of the motor effect is F=BIlsin(θ ), where F is the force, B is the magnetic field strength, I is the current through the wire, l is the length of the wire that is in the magnetic field, and θ  is the angle between the wire and the magnetic field lines.

The motor effect can be demonstrated by putting a current-carrying wire between the poles of a horseshoe magnet. The wire should experience a force, which will deflect it a little bit.

The motor effect happens because there are charged particles in the current-carrying wire, and those charged particles experience a magnetic force in the magnetic field. The charged particles push the whole wire in the direction of that force.

## Final Motor Effect Quiz

Question

Describe the motor effect.

The motor effect is the magnetic force on a current-carrying wire in a magnetic field.

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Question

What is the underlying cause of the motor effect?

The magnetic field around a current-carrying wire interacts with an external magnetic field to produce a force on the wire.

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Question

What are the quantities in Fleming's left-hand rule?

Thumb = force
Pointing finger = magnetic field
Middle finger = current

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Question

If we put a 1 m long wire carrying a current of 5 A along the magnetic field lines of an external magnetic field of 1 T, what can we say about the force on the wire?

The force is zero because the current is parallel to the magnetic field lines of the external magnetic field: there is no component of the current that is perpendicular to the magnetic field.

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Question

Name 2 ways of increasing the magnetic force on a current-carrying wire.

Possible ways are:
Increasing the current;
Increasing the magnetic field strength;
Increasing the length of wire in the magnetic field;
Adjusting the wire such that the angle between it and the magnetic field lines increases.

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Question

True or false? If the angle between the wire and the magnetic field lines doubles, the force on the wire doubles.

False

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Question

True or false? If the current doubles through the wire doubles, the force on the wire doubles.

True

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Question

True or false? If the magnetic field gets weaker, the force on the wire increases.

False

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Question

If a horseshoe magnet is positioned with its north pole above its south pole, and you lay a current-carrying wire between its poles with the current going from right to left, in which direction will the force on the wire be?

Towards you.

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Question

You place a wire horizontally in front of you with a current from left to right. It begins levitating. What can you conclude about the magnetic field close to the wire?

The magnetic field lines (partly) go horizontally away from you.

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