Force on a Current-Carrying Conductor

Introduction

In this article, you will find all the essential concepts related to the force on a current-carrying conductor.

We have introduced the concept of force on a current-carrying conductor, Characteristics of Magnetic Field, Magnetic Field, Magnetic Field due to current-carrying wire, and Magnetic Force.

Force on a current-carrying conductor is given by F = (nAL)qvd B. This is a standard equation to calculate magnetic force. We will go through deeply about this equation in the following pages.

Let us start with defining the Magnetic Field.

What is a Magnetic Field?

To understand the calculation of the force on a current-carrying conductor, first, 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 within the proximity of the magnet.

The magnetic field is the vector field in the region of an electric current magnet or altering electric field where the magnetic forces are noticeable. In a magnetic field, the subatomic particles with the -ve charge. This field can originate inside the atoms of magnetic materials or within the electrical wires or conductors.

Magnetic field lines

They are characterized using magnetic field lines. Magnetic field lines are a pictorial tool used to picture the strength and the direction of the magnetic field.

They can be drawn using a compass needle. Place the compass needle in one direction on a piece of paper that is positioned near the magnet and mark the direction where the needle points. Now move the compass needle in another position and repeat the same process. When we join the points, it indicates the magnetic field lines.

What are the Characteristics of Magnetic Field?

There are some characteristics of magnetic field lines. They are listed below:

• The tangent drawn to the magnetic field lines provides the direction of the magnetic field.
• The viscosity or 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 characterized 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.

What is a 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 normally 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 knew that lightning was a kind of electricity and also the proof that the working of a compass is established on the earth’s magnetic field. This indicated a relationship between the two, the magnetic field and the moving electric charge (current).

What is magnetic force?

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

What is the force on a current-carrying conductor?

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 consistency 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, 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 B)

This is the force on a current-carrying conductor.

Conclusion

In this article, we have discussed the magnetic field and magnetic force. A magnetic field is an area surrounding magnetic objects. In other words, a magnetic field can be described as the diffusion of magnetic force around a magnetic material or object. They are characterized using field lines which is the pictorial tool.