Current loop as a magnetic dipole and its magnetic dipole moment

Introduction:

The idea of a circular loop as a magnetic dipole was found by Ampere. It was seen that a current-carrying circular loop forms similar magnetic lines of force as a magnetic dipole. It creates lines of forces that are circular towards the elementary portions of the current loop and almost straight towards the centre of the coil. This made Ampere deduce that all magnetic phenomena are caused due to circular electric current flow. The magnetic moment of a current loop is the magnetic field’s strength and orientation created by the circular current-carrying loop. To understand the idea of a circular loop and magnetic dipole, one must understand each term individually.

Magnet and magnetic fields:

Magnets and magnetic fields are concepts that are familiar to everyone and easily seen around us. The characteristics of magnetism are:

1. Similar poles are repulsive: When two north poles of bar magnets are brought close to each other, they tend to repel each other or move away.

2. Opposite poles are attractive: When two opposite poles, such as a north pole and south of two magnets, are brought close to each other, they tend to attract each other

3. North and south poles of a magnet cannot be isolated. This is because every magnet, when broken into pieces, will create a dipole from each piece, i.e., each piece of the magnet will have a north pole and a south pole

4. When a bar magnet is suspended freely, the north pole of the bar will point to the geographical north, and the south pole will point to the geographical south.

Understanding magnetic fields and magnetism is most straightforward by using the example of the most common phenomena of magnetism around us: the earth’s magnetic field.

Characteristics of magnetic field lines:

1. The field lines form continuous and closed loops

2. The tangent drawn from any field line will give the direction of the magnetic field at that point

3. The strength of the field in an area can be determined by the number of field lines crossing per unit area. More the number of lines, more is the strength of the field at that point

4. Magnetic field lines can never intersect

Magnetic dipole and magnetic dipole moment:

A magnetic dipole is a substance where two opposite magnetic poles (north and south) of equal strength are kept at a very little distance; these dipoles can be bar magnets, current loops, etc.

A magnetic dipole is equivalent to the flow of current around a loop. When an electron rotates around the positively charged nuclei, it forms a magnetic dipole. An element with the sum of all these dipoles cancels out makes a neutral element with no magnetic dipole. But in cases where the dipoles are not balanced, it creates a permanent magnetic dipole like iron. 

A magnetic dipole moment is the strength and orientation of the magnetic field created by the dipole. It can be defined as the ability of a magnetic dipole to align itself with the magnetic field outside. The magnetic moment of a dipole or a magnetic dipole moment can be defined as the maximum torque produced by a magnetic dipole per unit value of the magnetic field in the surrounding area.

It can be measured as:

τ = m × B

τ represents the torque

m represents the magnetic moment

B is the magnetic field outside

Magnetic dipole, i.e., the presence of both poles of a magnet, creates a magnetic field. For example, if a bar magnet breaks into two, the pieces will act as magnetic dipoles individually, where both pieces will contain a north and a south pole.

Current loop as a magnetic dipole:

When a current loop is considered a magnetic dipole, the current multiplied by the area of the circle is proportional to the magnitude of the magnetic dipole moment. 

The magnetic field created by a current loop has the following characteristics:

1. The lines are circular near the elements and are almost straight towards the centre of the circular current-carrying coil

2. The magnetic force lines seem to be entering from the lower end of the coil and leaving from the upper back. The lower end from which the lines appear to be entering is the south pole of the dipole. The upper end from which the lines seem to be leaving is the north pole of the dipole.

3. The direction of the dipole moment of the current loop will be in a direction perpendicular to the plane of the current-carrying loop.

4. The direction of the magnetic dipole is a vector with the magnetic field moving from the south pole to the north pole

The magnetic dipole moment of a current loop:

Let us consider a current loop that carries a current I in the area given as A. Then, the magnitude of m will be the magnetic moment of the current loop. Hence, the magnetic moment formula is: 

|m| = IA

When the coil has n number of loops, then the total magnetic dipole moment will be calculated as |m| = nIA

Current times of the enclosed area or energy divided by the magnetic flux density give the magnetic dipole moment of a current loop. 

The unit of a dipole moment is ampere-meter2 in SI systems of measurement.

 On the other hand, the unit for dipole moment of a current loop is erg/gauss in the cm-gm-sec electromagnetic system, where erg is the unit of energy and gauss is the unit of magnetic flux density.

Bohr’s magneton is considered a more convenient unit for measuring the magnetic dipole moment of the current loop and is equivalent to 9.27×10-24 ampere square metres.

Conclusion:

A current-carrying loop behaves like a magnetic dipole such as a bar magnet. The magnetic field lines created by the current-carrying loop are similar to the magnetic field lines created by a dipole. The field lines of the current loop seem to be entering from the lower face of the plane of loop, which is the south pole and leaves from the upper face of the plane of loop, which is the north pole. The field lines are closed loops near the elements and become straight near the centre of the enclosed plane or circle. The magnitude of the magnetic dipole of a current loop is known as its magnetic moment or magnetic dipole moment. The current loop as a magnetic dipole and magnetic dipole moment are concepts equivalent to the magnetic dipole moment of a simple magnet.