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# Induced Potential

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Have you ever wondered how dynamos and generators work? As you might already know, the motor effect causes a movement of a current-carrying wire through a magnetic field. Interestingly, this also goes the other way around: the movement of a conducting wire in a magnetic field induces a potential that causes a current to run through the wire! Learn about the essentials of induced potential in this article.

We recommend you make sure to understand the motor effect before reading this article. It will make induced potentials a lot easier!

## The meaning of induced potential

When a conductor is moving through a magnetic field, or when a stationary conductor is positioned in a moving magnetic field, the conductor sees a moving magnetic field. This causes (induces) a potential difference between the ends of the conductor.

An induced potential (difference) is the potential difference between the ends of a conductor caused by a moving magnetic field around the conductor.

## Induced potential in a wire

When a wire is conducting and part of a complete electrical circuit, an induced potential causes a current to run through the wire.

An induced current is any current that is the result of an induced potential.

This is the most common way that people use to make electricity from other energy sources: the kinetic energy of a magnet causes a changing magnetic field, which induces a current in a wire. This is the basic explanation of how generators and dynamos work.

The creation of an induced current is called the generator effect, or (electromagnetic) induction.

A generator making use of the generator effect to induce a current, Wikimedia Commons CC BY-SA 4.0.

In the figure above, a generator is used to produce a current and power a small light bulb. It consists of a loop of wire that is moved relative to a stationary, permanent magnet. A potential difference is induced in the conducting loop and hence a current is too. The current is then used to power the light bulb.

## The principle behind induced currents

An induced current running through a conducting wire produces its own magnetic field, which will interact with the original magnetic field. This interaction will always be such that the motor effect on the wire produces a force that goes against the movement of the wire.

An induced current is always in the direction such that the motor effect reduces the speed between the wire and the magnetic field.

You can remember this by thinking about the kinetic energy of the system being transformed into the energy that the current is carrying. If the induced current went the other way, you would have a way of getting energy out of nothing, which is impossible.

## Factors affecting induced potential

The only factor affecting the size of the induced potential difference, and therefore of the induced current, is how many magnetic field lines the wire encounters per unit time. In turn, the factors affecting this are:

1. the magnetic field strength, and
2. how quickly the magnet moves compared to the wire (or vice versa, remember these situations are equivalent).

The first factor will lead to a higher "density" of magnetic field lines, and the second factor will lead to crossing magnetic field lines at a higher speed. Both will cause the wire to encounter more magnetic field lines.

## The formula for induced potential

Although it is outside the scope of GCSE exams, we can make these statements more quantitative.

The induced current through a conducting wire is directly proportional to how many magnetic field lines it encounters per unit time, so:

.

This equation makes it clearer that a magnetthat is twice as strong as magnetwill induce a current twice as large as magnetwill if the rest of the setup is the same. It also makes it clear that doubling the velocity of the wire will double the induced current through it in any given situation. Note that this worded equation only tells us how large the induced current is up to a constant, so it doesn't say anything about the directions of the quantities involved, and we can only make relative statements (doubling this will double that etc) instead of absolute statements (a magnetic field strength of this and that velocity will induce this current etc).

## Induced potential examples

There are some very insightful examples of induced potential differences and their induced currents.

### Horseshoe magnet and wire

The simple example of a horseshoe magnet and a wire can be enlightening. The figure below illustrates a horseshoe magnet with its north pole above its south pole, and a conducting wire lying horizontally between the poles of the magnet. If we pull the wire towards us, then there will be an induced current such that the wire will struggle against our pull. Thus, the motor effect causes a force away from us. We pick our favourite hand rule and conclude that the induced current runs from left to right.

Pulling a wire out of this horseshoe magnet will induce a current from left to right through the wire, Arjan van Denzen - StudySmarter Originals.

### Bar magnet and coil

A bar magnet can also induce a current in a coiled wire, see the figure below. On top, we see that we move a south pole closer to the coil, so the coil wants to stop this motion and produce a south pole close to the magnet. The coil does this by producing an induced current, and the right-hand rule tells us that the Ampere meter measures a current to the right, as indicated. On the bottom, we see that we move a north pole further away from the coil, which has the same effect as moving a south pole closer to the coil: the magnetic field changes in the same way. Therefore, we measure a current in the same direction as on top.

The movement of the magnet induces a current in the circuit in the direction of the arrow, adapted from image by Aaronming CC BY 4.0

## Induced Potential - Key takeaways

• An induced potential difference is the potential difference between the ends of a conductor caused by a moving magnetic field around the conductor.
• An induced current is any current that is the result of an induced potential difference, and its creation is called the generator effect, or (electromagnetic) induction.
• An induced current is always in the direction such that the motor effect reduces the speed between the wire and the magnetic field. Otherwise, you would have infinite energy.
• The only factor affecting the size of the induced potential, and therefore of the induced current, is how many magnetic field lines the wire encounters per unit time. This is affected by the magnetic field strength and by the speed of the wire relative to the magnetic field.
• Examples of induced currents are:
• If you try to pull a conducting wire out of a magnetic field, the wire will pull against your pull.
• If you try to pull a magnet out of a coiled wire, the magnet will pull against your pull.

An induced potential (difference) is the potential difference between the ends of a conductor caused by a moving magnetic field around the conductor.

The two factors affecting induced potential are magnetic field strength, and how quickly the magnet moves compared to the wire.

The formula quantifying induced voltage is called Faraday's Law.

Examples of situations with induced potentials are when you move a nail close to a magnet, or when you move a magnet close to a car.

The factors affecting the direction of the induced voltage are the direction of the relative motion between the magnetic field and the conductor, and the direction of the magnetic field lines themselves.

## Final Induced Potential Quiz

Question

What causes an induced potential?

Movement of a conductor through a magnetic field. Equivalently, a moving magnetic field around a conductor.

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Question

What is an induced current?

Any current that is caused by an induced potential difference.

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Question

Why is the creation of an induced current called the generator effect?

Because generators use this effect to convert kinetic energy into electrical energy.

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Question

How do you determine the direction of an induced current?

Induced currents always push against the motion between the wire and the magnetic field by using the motor effect. We use our favourite hand rule to determine the direction of the current given that we know the direction of the force it exerts.

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Question

What factors affect the induced potential?

The magnetic field strength, and the speed of the conductor relative to the magnetic field. Or, in other words, how many magnetic field lines the conductor comes across during a unit of time.

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Question

Suppose we push a wire through a magnetic field such that we induce a current in it. Which statement is true?

The wire will push against our push.

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Question

Suppose we push a magnet close to a closed circuit such that we induce a current in the circuit. Which statement is true?

The magnet will push against our push.

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Question

Two coils are standing next to each other, and a current is running through one of the coils. Will there be a magnetic force between the two coils?

No, because there is no moving magnetic field in this setup, so no induced currents are present in the other coil.

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Question

If you move two bar magnets with respect to each other, will there be an induced potential somewhere?

Yes, because bar magnets are conductors, and each magnet experiences a moving magnetic field from the other magnet.

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Question

If you move two bar magnets with respect to each other, will there be an induced current somewhere?

No, because the bar magnets are not part of a closed circuit.

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Question

Can we have an induced potential difference without an induced current?

Yes

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Question

Give an energy-based explanation for the fact that an induced current always pushes against original motion between wire and magnetic field.

A current carries energy, and this energy must come from somewhere. In this case, the energy can only come from the relative motion between the wire and the magnetic field.

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Question

Can there be an induced current without an induced potential?

No

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Question

If you drop a bar magnet down a long tube made of coiled wire, will it fall faster than, slower than, or at the same rate as dropping the same bar magnet without the coil?

Slower

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Question

If you drop a closed circuit down a space with a nonzero magnetic field, will it fall faster than, slower than, or at the same rate as dropping the same closed circuit down a space without a magnetic field?

Slower

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