Magnetic Dipole Moment of an Electric Circuit

Observable magnetism can be understood through the concept of magnetic dipole moment. The most intuitive definition of a dipole consists of two points that are equally charged but opposed. A magnetic field results from the interaction between these two charged monopoles. 

Magnetic dipole moment measures the torque experienced by a material in a magnetic field, which is determined by the pole strength and the distance between the poles. This is the opposite of the electric dipole moment, which measures the separation of positive and negative charges in a system.  

Magnets or other objects creating a magnetic field are measured by their magnitude, representing the magnet’s orientation and its strength. A few of these objects have magnetic moments, including loops of electric current (such as electromagnets), elementary particles (as electrons), permanent magnets, various molecules, and several astronomical objects (such as planets, certain moons, stars, etc.). 

Magnetic Dipole

Magnets or other objects that emit magnetic fields have a magnitude that indicates the orientation of a magnet and its strength. Magnetic moments refer to magnetic dipole moments, which are the constituents of magnetic moments that showed by magnets. 

An electromagnetic dipole consists of two magnetic poles separated by a small distance. There are the dipole moments of a magnet whose sizes are determined by flux density of the magnet and the current time’s energy, or it can be region. It is an ampere-square metre (unit of energy) per gauss (unit of density) in the centimetre-grams-seconds system of the electromagnet. 

In metres-kilograms-seconds-ampere, a magnetic dipole moment is an erg that is the energy’s unit Gauss law per that unit of flux density of magnet. 1-ampere per meter2 is equal to 1 thousand gausses per ergs.

Theory of Magnetic Dipole

Rather than being represented as a series of terms, the magnetic field of magnets is represented by a set of terms that is more complex (with finer angular details). Three of the first terms referred to series are the monopole (depicting an isolated magnetic north pole or south pole), a dipole (depicting two opposite and equal poles), and also the quadrupole (depicting four poles combining to form opposite and equal dipoles). 

Every term’s magnetic field decreases with distance progressively so that the first non-zero term will take over at large enough distances. Magnetic dipoles occur when dimensions of a source are reduced to zero maintaining a continuous moment. So far, no monopoles of magnets have been observed experimentally. 

Magnetic Dipole Formula

Magnetic Dipole Moment is tiny loops of current that act like tiny magnets. M, the magnetic dipole moment of that tiny magnet, can be calculated by giving the unit – Ampere metre square, which is said to be the magnetic dipole moment. The magnetic dipole moment is a vector quantity according to the right-hand thumb rule.

A magnetic field alignment vector links the object’s alignment torque and the magnetic field vector itself. The magnetic dipole moment formula can be calculated this way. 

Torque on magnetic dipole

Ꞇ  = M×B

Work done in rotating a magnetic dipole in a uniform magnetic field W=MB(cosӨ₁-cosӨ₂)

Potential energy of a magnetic dipole is the work done in rotating the dipole through an angle θ with respect to a direction perpendicular to the field .

U=-MBcosθ=-M.B

An unknown sample’s magnetic moment is measured using this definition. The magnetic dipole moment associated with a loop of current can be calculated as the product of the current times the area that the loop has. This definition also allows for the calculation of the projected magnetic dipole moment for any known macroscopic current sharing. This definition can also be used to calculate the magnetic moment thermodynamically. 

Magnetic Dipole of Current Loop

The calculation of the magnetic field is independent of the shape of the loop for distances R r (the loop radius). Only the area and the current are involved. Also, the loop radius θ). Current in the loop is designated by ‘i’, loop area by A, and radial distance by R. Polar angle, ф, is determined by the Z-axis. 

Magnetic dipoles produce fields similar to those produced by tiny bar magnets. Magnetic dipole moment is defined as vectors pointing out of the current loop plane, whose magnitude equals the product of the loop area and the current. By utilising the direction of the currents, a right-hand rule determines the direction of the area vector and thus the direction of the magnetic dipole moment.

Conclusion

Magnetic fields distanced away from the source are predicted by both types of dipoles (current loops & magnetic poles). However, in the interior source region, it predicts magnetic fields differently. Between the two poles, the magnetic field opposes the moment of the magnet (i.e., it faces from negative to positive charge), and inside a loop of current, it opposes the magnetic field.

It should be noted that the term magnetic moment refers to the magnetic dipole and magnetic dipole moment of a system, which is the component of the magnetic moment that can be represented by the magnetic north and south poles. Small magnets or large distances are sufficient for the magnetic dipole component. The dipole moment may not be enough to describe the behaviour of prolonged objects, and higher-order expressions (such as the magnetic dipole moment) may be required.