# Magnetic moment class-12, definition, units, and measurement

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In the previous article, we have discussed the magnetic force that acts between the two parallel straight current-carrying conductors. In this present article, we will discuss the magnetic dipole moment in detail, so let’s get started…

Inside Story

## Magnetic moment class-12

The magnetic moment also called magnetic dipole moment is the magnetic strength and orientation of a magnet or any other object that produces a magnetic field. Did you understand? what above statement say? if not, let’s understand it in simple words. The above statement says that when you throw or place a magnet or any magnetic material in the region of a uniform magnetic field then the magnetic materials experience a torque (angular force) which aligns the magnet in such a way that it becomes stable. The magnet or any magnetic material which produces a magnetic field becomes stable when it aligns itself parallel to the magnetic field lines because at this orientation angle between the magnetic field and magnet is 0° or 180° so it experiences zero torque.

In other words, we can say, magnetic moment is the ability of the magnetic materials to align itself in such a way that it expriences zero torque in external uniform magnetic field. Fig. 1, the magnetic moment of a bar magnet in an external uniform magnetic field, source: toppr.com

There are various magnetic objects which have a magnetic moment. The object which has the magnetic moments includes electric current loops such as (electromagnets or solenoids), permanent magnets, subatomic particles such as electrons, various molecules, and many astronomical objects such as planets, moons, stars, etc.

Usually, the term magnetic moment normally refers to the term magnetic dipole moment, as we have said above magnetic moment is also called magnetic dipole moment, why? It is because the component of the magnetic moment can be represented by an equivalent magnetic dipole. A magnetic dipole is an equal and opposite pole (north and south) of a magnet separated by a very small distance. The component of a magnetic dipole is sufficient for small enough magnets or large enough distances.

The magnetic dipole moment of an object can be defined as the torque experienced by an object when placed in a specific magnetic field. The same applied magnetic field can create more torque on objects with a large magnetic moment. The strength and direction of the torque experienced depend not only on the magnitude of the magnetic moment but also on its direction relative to the direction of the magnetic field. Consequently, the magnetic moment can be viewed as a vector. And it is directed from the south pole to the north pole inside any magnet.

The magnetic field of a magnetic dipole is proportional to its magnetic dipole moment. The dipole component of the object’s magnetic field is symmetric to the direction of its magnetic dipole moment and decreases in proportion to the cube, and the reciprocal of the distance from the object. [latexpage]

## Definition, units and measurements

### Definition of magnetic moment

Magnetic moment can be defined as the magnetic strength and orientation of a magnet or any other magnetic material that produces a magnetic field when it is exposed to the external magnetic field. In simple words, it is the measure of the ability of the magnetic material to align itself with the external magnetic field.

The magnetic moment is typically expressed as a vector relating the aligning torque working on the magnetic material from the externally applied magnetic flux to the field vector itself. The relationship is given as- $${\boldsymbol {\tau }}=\mathbf {m} \times \mathbf {B}$$ In the above equation, τ is the torque acting on the dipole, B is the external magnetic field, and m is the magnetic moment. For a current-carrying loop, this definition leads to a magnetic dipole moment equal to the product of the current flowing in the loop and the loop area. $$\mathbf{m}=IA$$ where $I$ is the current flowing in the loop and $A$ is the area of the loop. Additionally, this definition allows the expected magnetic moment to be calculated for any known macroscopic current distribution.

### Units of magnetic moment

The SI unit of the magnetic moment is $A\cdot m^2$, where A is ampere (SI unit of electric current) and m is meter (SI unit of distance). We can derive many other units for magnetic moment that is equivalent to original base unit including- $${\text{A}}{\cdot }{\text{m}}^{2}={\frac {{\text{N}}{\cdot }{\text{m}}}{\text{T}}}={\frac {\text{J}}{\text{T}}}$$ Where N is newton (SI derived unit of force), T is tesla (SI derived unit of magnetic flux density), and J is joule (SI derived unit of energy). Although torque (N·m) and energy (J) both are dimensionally equivalent but note that torques are never expressed in units of energy because they are different terms and have different meanings. Torque is angular force whereas energy is the product of force and displacement.

### Measurement of magnetic moment

The magnetic moments of materials are generally measured with a device called a magnetometer. But not all magnetometers are used to measure magnetic moments. Some magnetometers are configured such that they can measure magnetic fields instead. If the magnetic field surrounding an object is known well enough, then from the knowledge of this magnetic field we can measure the magnetic moment of the respective objects.

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