Parallel Currents: UNIZOR.COM - Physics4Teens - Electromagnetism - Magnetism and Electric Current
Channel: Zor Shekhtman on UNIZOR Education
Date: 2020-06-03

Unizor - Physics through a Looking Glass of Mathematician

Notes to a video lecture on http://www.unizor.com

Two Parallel Straight Line Currents

Let's examine a behavior of two ideally long and thin parallel wires, each carrying an electric current.

As we know, since the wires carry electric current, there is a magnetic field around each of these wires. It has circular form. The direction of the magnetic field lines is determined by the corkscrew rule or the right hand rule.

Each circular magnetic field line around the first wire and any tangential to it, that is the vector of magnetic force, belong to a plane perpendicular to this wire. Since the second wire is parallel to the first one, any tangential to any magnetic field line of the first wire is perpendicular to the second wire.

Since the second wire's electric current is perpendicular to the direction of the magnetic field lines of the field produced by the first wire, the second wire is under the Lorentz force produced by the magnetic field of the first wire. Using the right hand rule for the second wire and the first one's magnetic field lines, we determine the direction of this Lorentz force. It appears to be directed from the second wire towards the first one.

The wires are in symmetrical positions, so exactly the same logic can be applied to the first wire in the magnetic field of the second wire. As a result, the Lorentz force produced by the magnetic field of the second wire attracts the first wire towards the second one.

Now we see that both wires attract each other, which is caused by the Lorentz force exerted on each of them from the magnetic field of the other one.

Let's arrange a similar experiment having electric currents in the wires to go in opposite directions. Let the first wire's current to go the same way as before, but the direction of the electric current in the second wire to be opposite.
The logic about circular magnetic field lines around any wire and perpendicularity of the electric current of one wire to the magnetic field lines of the opposite one remains the same. The only difference is that, when we apply the right hand rule to determine the direction of the Lorentz force, the result will be opposite than before, the Lorentz force will push the second wire away from the first one.

Analogous result will be when we consider the electric current in the first wire in the magnetic field of the second wire. The Lorentz force in this case will also be repelling.

The conclusion of these experiments is that
(a) parallel wires carrying electric charge will attract each other if the currents are in the same direction;
(b) parallel wires carrying electric charge will repel each other if the currents are in the opposite directions.

This effect was studied by Ampere and the mutual attraction or repulsion of two parallel wires carrying an electric current is often referred to as the Ampere force.

Contemporary definition of an 1 ampere (1A) as a unit of electric current is 1 coulomb per 1 second (1C/1sec) with a unit of charge 1 coulomb defined based on the charge of certain number of electrons.

At the time of Ampere's experiments with parallel wires scientists did not know about electrons and could not measure the electric current in the same terms as we do now.
But Ampere's experiments have opened the way to measure the electric current by measuring the purely mechanical characteristic of the force of attracting or repelling between the wires carrying the electric current. So, the first definition of a unit of current was based on measuring the Ampere force between the two wires.