Ampere force

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

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

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

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 $1\mathrm{A}$ parallel to each other separated by a distance of $1\mathrm{m}$. Then the force between them will be equal to$2\times {10}^{-7}\mathrm{N}$. This can also be used to define the value of $1\mathrm{A}$. We know that ampere is the standard unit of current.$1\mathrm{A}$can also be defined as the current flowing through parallel wires at a distance of$1\mathrm{m}$from each other which produces a force of$2x{10}^{-7}\mathrm{N}$.

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.