Current Loop

Introduction

The current loop is the flow of current that leads to the development of magnetic dipole moment. A simple definition of the magnetic moment of a current loop – a product of the area of the rectangular loop and current that flows around it is known as the magnetic moment of a current loop. However, the direction of the magnetic moment is given by the right-hand thumb rule formula. Before we understand magnetic dipole moments in detail, let’s have a look at what a simple magnetic moment is.

A magnetic moment defines the magnetic strength and magnetic orientation that leads to the production of a magnetic field. Also, when a small distance separates the North and South poles of a particular magnet, it develops a magnetic dipole moment. Want to learn more about the magnetic moment of a current loop? Let’s scroll through the article right away!

What Is a Magnetic Dipole Moment? 

Magnetic dipole moment, also known as magnetic moment, defines the strength of the magnetic dipole. In other words, it is a measure that defines the ability of the magnet to align itself with the applied external magnetic field. When the applied external magnetic field is uniform, the magnitude of the magnetic dipole moment is directly related to the amount of torque applied on the dipole.

This condition occurs when the dipole and magnetic field angle is 90°. Alternatively, when the magnetic dipole is in the current loop, the magnitude of the magnetic dipole moment is directly related to the product of the current and the size of the area enclosed by the loop. It is a vector quantity whose direction is perpendicular and away from the positive charge flow. If we consider the closed current loop as a small magnet with two poles, the direction of the vector will be from the south to the north pole. 

Dipole moment has a unit ampere- metre square in metre–kilogram– second–ampere measurement system. And it is erg per gauss in centimetre–gram–second measurement system. 

Where erg = (unit of energy) 

Gauss = (unit of magnetic flux density)

Magnetic Moment Formula

Generally, there are two ways by which magnetic dipole moments are produced. These are by the motion of electric charge, or it is due to spin angular momentum. A magnetometer is a device used to measure the magnetic moment in a dipole or current loop. The formula of magnetic moment is directly related to the two most important quantities, that is, the torque of an object and the magnetic field. Here is the mathematical representation of the magnetic moment formula:

τ = M x B 

τ is the symbol of the torque of the object, M is the symbol of the magnetic moment that is developed in the current loop, and B is the applied external magnetic field. 

Unit of Magnetic Moment 

As mentioned above, the magnetic moment in a current loop is the product of two important quantities – Current flowing through the closed-loop and the area enclosed by it. Here is the mathematical representation of the magnetic moment in a current loop in unit form.

M = I A

As per the formula, the current (I) is measured in amperes and area (A) is measured in meters2. According to this, the result came out to be Amp-m2. Suppose we suggest the formula in terms of moment and torque. This formula becomes J/T, where J stands for Joules, in which we measure torque, and T stands for Tesla, in which we measure the magnetic field. 

Hence, 1 Amp-m2 = 1 J T-1.

Derivation of Magnetic Dipole Force 

Both of the magnet poles are directly related to the force on the magnetic dipole. When the magnetic dipole is kept under the influence of an external magnetic field, the two forces are the same in magnitude but differ in direction. Meaning the force applied on the north pole is along the magnetic field and is denoted by mB.

On the other, the force applied on the south pole is opposite to the magnetic field and is again denoted by mB. When both the force acts similarly, they form a parallel couple. In turn, it helps the magnet rotate in the clockwise direction. When the magnet starts to rotate, a net torque is generated in the bar magnet. Here is the mathematical representation of magnetic dipole force. 

τ = mB × 2L sin θ

Where τ is the moment of the parallel couple in the bar magnet, mB is the force applied to the poles of the magnet,  θ  is the angle formed between the magnet and the magnetic field. In another form, the magnetic dipole force is represented by 

τ = M × B

Different Uses of Magnetic Dipole Moment

Here are the different applications in which magnetic dipole moment is used:

• One of the main applications in which the dipole moment is used in calculating the percentage ionic character in ionic or covalent heteronuclear diatomic compounds
• It helps distinguish between cis- and trans- isomers
• The dipole moment is large in cis- isomer, whereas in trans- isomer, the dipole moment is small
• The bond angle can be easily calculated with the help of the dipole moment
• The size, structure and arrangement of molecules in any chemical bond are determined by dipole moment
• The ortho, meta and para isomers are distinguished with the help of dipole moments
• In the case of a para isomer, the dipole moment is zero
• Also, the dipole moment of meta isomers is smaller than the dipole moment in ortho isomers

Conclusion

The magnetic moment in a current loop is a way to determine the magnet’s strength. We hope this article will help you get adequate knowledge about magnetic dipole moment in the current loop, magnetic dipole moment formula, and other important information.