# Magnet, wire and Newtons third law

• Zaigon
In summary, when a bar magnet and an infinite wire carrying a current are positioned in free space with the wire below the north pole of the magnet, there are two forces at play. The magnetic field from the wire creates a torque on the magnet, causing it to rotate, but the third law of motion states that the force on the magnet is equal and opposite to the force on the wire. This can be explained by the energy of the magnet in the magnetic field, which is dependent on the horizontal position of the magnet and results in a force pointing in the opposite direction of the force on the wire.
Zaigon
I have been thinking about a bar magnet and an infinite wire in free space. The wire is positioned below the north pole of magnet and carries a current.

1) The force from the magent on the wire: Due to the magnetic field, the Lorentz force on the electrons in the wire creates a force on the wire which is directed perpendicular to the plan containing the wire and the magnet.

2) The force from the wire on the magnet: The magnetic field from the wire creates a torque on the magnet which tends to make it rotate, but is there any net force on the maget? What about Newtons third law here?

Will the magnet be accelerated in the opposite direction of the acceleration of the wire? And why?

The third law gives a simple answer to this question which is that the force on the magnet is equal and opposite to that on the wire.

That I get, but I was interested in an explanation of this force.

In the meantime I have figured out how to explain it: The energy of the magnet in the magnetic field from the current is the dot product of the magnetic moment with the magnetic field. And this quantity depends on the horizontal position of the magnet (transverse to the wire), so the force (as the gradient of the energy) points in this direction, opposite to the force that the wire feels.

## What is a magnet?

A magnet is a material or object that produces a magnetic field. This field is responsible for the force of attraction or repulsion between two magnets, as well as the interaction between a magnet and other objects made of magnetic materials.

## How does a wire interact with a magnet?

When an electric current flows through a wire, it creates a magnetic field around the wire. This magnetic field can interact with the magnetic field of a nearby magnet, resulting in a force that can either attract or repel the two objects.

## What is Newton's Third Law?

Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction. This means that when two objects interact, the forces they exert on each other are equal in magnitude but opposite in direction.

## How does Newton's Third Law apply to magnets and wires?

When a wire interacts with a magnet, the wire exerts a force on the magnet and the magnet exerts an equal and opposite force on the wire. This is an example of Newton's Third Law in action.

## What are some real-world applications of magnets, wires, and Newton's Third Law?

There are many applications of magnets, wires, and Newton's Third Law in everyday life. Some examples include electric motors, generators, MRI machines, and speakers. These all rely on the interaction between magnets and wires to produce motion or electricity, and Newton's Third Law explains the forces involved.

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