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# Ampere force

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We know that a current-carrying conductor produces a magnetic field and a force. But how do we calculate this force and what does this depend on. And what if two current-carrying conductors are placed close to each other. Lucky for us, physicist André-Marie Ampère discovered that a wire carrying a current will attract or repel another wire within its vicinity. This single discovery led to the formation of what we know today as electromagnetism. The basic unit of current was rightly named after Ampere to honour his work. His experiments and work in electromagnetism led to the formulation of a law called Ampere's force law. This law signifies the dependencies between the induced force and other factors such as the intensity of current and the length of the wire. In this article, we go through Ampere's force law and the laws that formed its basis. We will also look at its equation and work on a few examples. Happy Learning!

## Ampere force law

Ampere force law states that the forceof attraction or repulsion between two current-carrying wires is proportional to their lengths and the current flowing through them.

The direction of the magnetic force depends on the direction of the current in both the wires, Wikimedia Commons CC-BY-SA-4.0

If the direction of the flow of current is the same in both the wires then the force is attractive. If the current flows in opposite directions then the force is repulsive. The fundamental basis of the Ampere force law is provided by the following laws that existed previously.

### Right-hand thumb rule

The Right-hand thumb rule is depicted here; it shows the relationship between the current passing through a wire and the magnetic field it produces, Wikimedia Commons CC-BY-SA-4.0

The rule states that if you hold a current-carrying conductor with the thumb pointed at the flow of current, then the direction in which the fingers curl will represent the magnetic field around it.

### Fleming's left-hand rule

Fleming's left-hand rule shows the direction of the thrust on a conductor carrying a current in a magnetic field
, Wikimedia Commons CC-BY-SA-3.0

The rule states that if we stretch the thumb, middle finger, and index finger of the left hand in such a way that they make an angle of 90 degrees. Then the thumb will point in the direction of the induced force the middle finger will point in the direction of the current and the Index finger will represent the direction of the magnetic field

## Ampere's Force Experiment

Ampere first discovered the phenomenon of a force acting between two wires. He noticed that a compass needle would deflect perpendicularly when brought close to a current-carrying conductor. His next experiments consisted of studying the force acting on two current-carrying wires by varying:

• The current passing through them

• The direction of the currents

• The distance between the wires and

• Finally, the length of the wires

He found that two parallel wires carrying current in the same direction will attract each other and repel if the directions of current passing through them are opposite. And if the two wires are placed perpendicular to each other, then the force acting between them will be zero.

## Ampere's Force Equation

There is a complicated mathematical derivation for the force between two wires which you do not need to know for your GCSE exam!

We know that the Ampere's force is proportional to the length of the wire and the current passing through them. The Amperes force between two parallel wires can be obtained as follows:

Ampere's force between two parallel wires, Wikimedia Commons

If we place two wires carrying a current of parallel to each other separated by a distance of . Then the force between them will be equal to. This can also be used to define the value of . We know that ampere is the standard unit of current.can also be defined as the current flowing through parallel wires at a distance offrom each other which produces a force of.

There are a few interesting properties of the Ampere's force.

• The force is attractive in nature when the current in both the wires flows in the opposite direction.

• The force is repulsive in nature when the current flows in the same direction.

• The force is zero when the two wires are perpendicular to each other.

• The force increases as the magnitude of current in the wires increases.

• It is also inversely proportional to the distance between the wires.

## Ampere's Longitudinal Force

Ampere later discovered an additional force that would act along the axis of the current-carrying wire. This force is called Ampere's longitudinal force. This tensile force tended to stretch wires carrying large currents. This has also been referred to as Ampere's tension. The wire when exposed to its magnetic field experiences a longitudinal force that stretches it.

## Ampere's Force - Key takeaways

• Ampere force law states that the force of attraction or repulsion between two current-carrying wires is proportional to their lengths and the current flowing through them.
• A current-carrying conductor placed in a magnetic field will experience a force that is perpendicular to both fields. The direction of the force depends on the direction of the flow of current.
• can also be defined as the current flowing through parallel wires at a distance of from each other which produces a force of .
• Ampere later discovered an additional force that would act along the axis of the current-carrying wire. This force is called Ampere's longitudinal force.

Ampere's equation for the force between two parallel wires is given by F/L= 2x10-7 x (I1xI2)/r

where F is Ampere's force, I1 and I2are the currents flowing through both wires, L is the length of the wires and r is the distance between them.

Ampere's force is the force of attraction or repulsion between two current-carrying wires

1 ampere can be defined as the current flowing through parallel wires at a distance of 1 m from each other which produces a force of  2x10-7 N

Ampere's force law gives the force per unit length between two parallel wires, F/L= 2x10-7 x (I1xI2)/r, where F is Ampere's force, I1 and I2are the currents flowing through both wires, L is the length of the wires and r is the distance between them.

## Final Ampere force Quiz

Question

What is ampere's force?

It is the force of attraction or repulsion between two current-carrying wires.

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Question

In the right-hand thumb rule thumb shows the direction of ...

Force experienced by the current carrying conductor.

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Question

1 ampere can also be defined as the current flowing through parallel wires at a distance of 1 m from each other which produces a force of ...

2x10-7 N

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Question

How do you figure out the direction of the magnetic field around a current-carrying wire?

Right-hand thumb rule

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Question

The Ampere's longitudinal force acts parallel to the wire.

True

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Question

The magnitude of Ampere's force when two wires are perpendicular to each other is ...

Zero

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Question

The Ampere's force when the current in the wires flows in opposite direction is ...

Attractive

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Question

The Ampere's force is ...

Proportional to the current in the wires

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Question

The ampere's law is used to find the ...

Force between two wires

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Question

The force between two wires is repulsive when ...

The direction of the current is the same.

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Question

Ampere's force is always attractive in nature.

False

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Question

The direction of the ampere's force depends on the ...

direction of flow of current in both the wires.

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Question

Ampere's law does not depend on the type of charged particle flowing. True or false?

True

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Question

Which type of force is Ampere's law?

Electric

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