Force On A Current-Carrying Conductor

Introduction

In 1820, HC Oersted proved that electric current creates a magnetic field. Michael Faraday observed this and believed that if an electric current can create a magnetic field, then a magnetic field can also create a current. In 1831, Faraday showed the world that if a magnet is moved inside a copper coil, very little electric current is induced. This gave a new direction to the research on magnetism and its forces.

Magnetic Field

To understand the calculation of the force on a current-carrying conductor, we need to understand the magnetic field. The magnetic field is an area or an invisible space around a magnetic object or moving electric charge or material within which the force of magnetism works. The fields are generated or created when the electric current/charges move.

This field can originate inside the atoms of magnetic materials or within the electrical wires or conductors.

Magnetic Field Lines

Magnetic field lines are imaginary lines found around a magnet that define the direction and strength of the magnetic field. In a bar magnet, these lines are denser at the poles; hence the magnetic field at the poles will be greater than at the centre.

Characteristics of Magnetic Field

Some characteristics of magnetic field lines are as follows:

• The tangent drawn to the magnetic field lines provides the direction of the magnetic field
• The closeness of the field lines is immediately proportionate to the strength of the field
• Magnetic field lines seem to originate or start from the north pole and eliminate or merge at the south pole
• The path of the magnetic field lines is from the south to the north pole Inside the magnet
• Magnetic field lines do not bisect one another
• Magnetic field lines construct a closed-loop
• Magnetic field lines have both magnitude and direction at any point on the magnetic field. Hence, they are characterised by a vector
• They indicate the direction of the magnetic field
• The magnetic field is powerful at the poles because the field lines are heavier near the poles

Magnetic Field due to the Current-Carrying Wire

The magnetic field is commonly defined as an area where the force of magnetism works. This force of magnetism is typically generated as an outcome of shifting charges or some magnetic element. H. C. Oersted was the first scientist who discovered that a current-carrying conductor generates a magnetic impact around it. For example, the effect of lightning when it strikes a ship causes the breakdown of compass needles, disturbing the navigation system. We know that lightning is a kind of electricity and this provides proof that a compass’s working is established on the Earth’s magnetic field. This indicates a relationship between the magnetic field and the moving electric charge (current).

Magnetic force

The moving charge does not feel any force when parallel to the magnetic field. Magnetic force is a force that occurs due to the interchange of magnetic fields. It can be both a repulsive and attractive force.

Effects of Magnetic Force on a moving charge in the existence of Magnetic Field

A charge ‘q’ moves with the velocity ‘v’ with an angle ‘θ’ in the field direction. Experimentally, we found that a magnetic force acts on the moving charge and is given by F=q (v x B). This is known as the Lorentz force law.

Force on a Current-Carrying Conductor in Magnetic Field

Now we will discuss the concept of the force as a result of the magnetic field in a straight current-carrying rod.

We contemplate a rod of identical length L and cross-sectional area A.

In the conducting rod, let the number density of portable electrons be given by n.

Then the sum of the number of charge carriers is given by nAI, where I refer to the steady current in the rod. The drift velocity of each portable carrier is presumed to be assigned as vd. When the conducting rod is positioned in an outer magnetic field of magnitude B, the force pertained on the portable charges or the electrons can be given as:

F = (nAL)qvd B

Where q refers to the value of charge on the mobile carrier.

As nqvd refers to the current density j

and A×|nqvd| = I, the current through the conductor

Hence, we can write:

F = [(nqvd)AL} B = ILB

This force in vector form can be written as

F = I (L x B)

This is the force on a current-carrying conductor.

Conclusion

In this article, we have discussed the force on a current-carrying conductor. Moving current generates a magnetic field around it and behaves like a magnet, and a magnet experiences some force when placed in this magnetic field. In the same way, the magnet also exerts a force on the current-carrying conductor, which Fleming’s left-hand rule can determine.