Magnetic Dipole Moment - Definition, Formula, FAQs

Edited By Team Careers360 | Updated on Nov 12, 2024 11:54 PM IST

Magnetic dipole moment may be a quantity that shows the strength and direction of the magnetic dipoles. This will be represented by the torque that a medium experiences when added to a magnetic flux and therefore the stronger the torque. As there is both force and orientation/direction, the dipole moment may be a vector.

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What is Magnetic dipole?
What is a Magnetic moment?
Magnetic dipole moment:

Magnetic Dipole Moment - Definition, Formula, FAQs

In this article, we will discuss what is Magnetic dipole? Definition of Magnetic dipole. What is magnetic dipole moment? Give its formula and SI unit with examples. How to find magnetic dipole moments? What is the unit and symbol of magnetic moment? Direction of Magnetic moment and Magnetic dipole moment.

What is Magnetic dipole?

Magnetic dipole is an ordering of two separate magnetic poles of equal pole strength separated by a really small distance, e.g., a little magnet, a magnet, a current carrying loop etc.

NCERT Physics Notes:

Dipole moment

The most elementary magnetic structure always behaves as a pair of two magnetic poles of opposite types (north and south or positive and negative) and of equal strengths; isolated magnetic poles are not observed. Thus, the definition of Magnetic dipole is a pair of two magnetic poles of opposite types and equal strengths a finite distance apart. A bar electret is an example of a magnetic dipole.

Magnetic lenght, axis and equator of a bar magnet

Since the magnetic field lines are closed loops, the positions of the poles cannot be accurately determined. In the case of a bar magnet, the positions of the poles are conjectured to be the points inside the magnet where the field lines appear to meet when extrapolated. Now we see,

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What is a Magnetic moment?

The moment of a magnet is the magnetic force and direction of a magnet or other object that creates a magnetic field. Examples like of body that possess magnetic moments are: loops of electrical current (such as electromagnets), permanent magnets, elementary particles (such as electrons), various molecules, and lots of astronomical bodies like (such as some moons, many planets, stars, etc). Now we define a magnetic moment as a vector that relates the placing torque on the object via an externally applied magnetic field to the field vector itself. The symbol of magnetic moment is μ. Magnetic moment formula in physics is given by: τ=μ ×B

Where, τ = torque acting on the dipole

B = external magnetic field

μ = magnetic moment

And this is also what we say about the magnetic moment formula in class 12th.

The unit for magnetic moment in Systeme International d'Unites of Units (SI) base units is A⋅m², where A is ampere (SI base unit of current) and m is meter (SI base unit of distance). This unit has counterpart in other SI derived units including:

A⋅m²=N.m/T= j/T

Where, N = Newton (SI derived unit force)

T = Tesla (SI derived unit of magnetic flux density)

J = Joule (SI derived unit of energy)

While torque (N.m) and energy (J) are dimensionally equal, torques are not at all expressed in units of energy. Now we understand how to find magnetic moments? By using example: Calculate magnetic moment of Fe²⁺_(aq)ion(Z=26).

Ans: The electronic configuration of Fe²⁺_(aq)ion is 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁶4s⁰

The total number of sparated electrons, n = 4

Magnetic moment is given by, $\mu=\sqrt{n(n+2)}B.M.$

$=\sqrt{24}$

= 4.9B.M.

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The direction of magnetic moment a magnet points from the south to North Pole of the magnet (inside the magnet). The magnetic fluxes of a dipole are directly proportional to its dipole moment.

Direction of magnetic moment

Magnetic dipole moment:

Now we see Magnetic dipole moment. Do you know? What is magnetic dipole moment?

Magnetic dipole moment is the product of the strength of either pole and therefore the magnetic length of the magnet. It’s a vector quantity and is represented by M.

When a magnetic dipole of magnetic dipole moment $\underset{M}{\rightarrow}$ is placed in a uniform magnetic field of induction $\underset{B}{\rightarrow}$ , it experiences a torque whose magnitude is

τ=MBsinθ

Where,θ= (smaller) angle between the magnet axis $\underset{B}{\rightarrow}$ . When the dipole I s placed with its axis at right-angles to the field, i.e, θ=90°,

Formula

τ=MB or M= $\frac{ \tau}{B}$

This is the magnetic dipole moment formula.

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Definition: The magnitude of the magnetic dipole moment of a magnet (or current-carrying coil) is defined as the magnitude of the torque that acts on it when it is placed with its axis at right-angles to a uniform magnetic field of unit induction. The electric/magnetic dipole moment nucleus is 0.

For a bar magnet, the magnetic dipole moment is directed from the south pole of the magnet to its north pole. For current loop, the magnetic dipole moment has the direction of the axial field of the current loop as given by the right-hand rule shown in Fig below: if the fingers of the right hand are curled in the sense of the current in the loop, the outstretched thumb gives the direction of the magnetic dipole moment.

Magnetic dipole moment- fingure rule

Dimensions: M= [L² I]

SI unit: the ampere.meter² (A.m²)

The direction/orientation of magnetic dipole moment is from South Pole to North Pole of a magnet. Considering the present loop as a small magnet, this vector corresponds to the direction from the south to the North Pole. Now we see, Circular current loop as a magnetic dipole behaves sort of like a magnet. Its magnetic flux lines also as north and south poles, a bit like a magnet. To place all this during a simpler perspective, imagine a clock. Now the clock completes one round from 12 - 12. That direction is what we call clockwise. So if the current is clockwise then the direction of magnetic flux lines are going to be inward.

Similarly, direction opposite to movement of clock is named anti-clockwise direction. So if current is occupation anti-clockwise direction the direction of magnetic flux lines are going to be in outward direction i.e. If current is in an anti-clockwise direction then the direction of magnetic flux lines is going to be in an outward direction. If current is in clockwise direction the direction of magnetic flux lines is going to be inward direction. And this is the answer of the question explain behavior of a current loop as a magnetic dipole.

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Frequently Asked Questions (FAQs)

1. What is magnetic field/flux?

The number of magnetic field lines passing through a surface, held perpendicular to the lines, is called the magnetic flux through the surface. SI unit is 1 Wb = 1N.m/A.

2. What is the pole strength of a magnetic dipole? State its dimensions and SI unit.

The pole strength (m) of a magnetic dipole is given by its magnetic dipole moment divided by its magnetic length.

m= M/2l

Dimensions: [m] = [LI]

SI unit: the ampere.metre (A.m)

3. A bar magnet of geometric length 12cm has a magnetic moment of 3 A.m2. Determine its pole strength.

The pole strength (m) of a magnetic dipole is given by its magnetic dipole moment divided by its magnetic length.

m= M/2l

Dimensions: [m] = [LI]

SI unit: the ampere.metre (A.m)

4. Explain behavior of a current loop as a magnetic dipole.

Circular current loop as magnetic dipole behaves sort of like a magnet. Its magnetic flux lines also as north and south poles, a bit like a magnet. To place all this during a simpler perspective, imagine a clock. Now the clock completes one round from 12 - 12. That direction is what we call clockwise. So if the current is clockwise then the direction of magnetic flux lines is going to be inward direction.

Similarly, direction opposite to movement of clock is named anti-clockwise direction. So if current is occupation anti-clockwise direction the direction of magnetic flux lines are going to be in outward direction i.e. If current is in an anti-clockwise direction then the direction of magnetic flux lines is going to be in an outward direction. If current is in clockwise direction the direction of magnetic flux lines is going to be inward direction. And this is the answer to the question that explains the behavior of a current loop as a magnetic dipole..

5. Is the dipole moment the same as magnetic moment?

They both are an equivalent. The strength of a dipole, called the dipole moment, could also be thought of as a measure of a dipole's ability to show itself into alignment with a given external magnetic flux . The term "magnetic moment" is a smaller amount used. A dipole arises via current loops.

6. Define magnetic dipole moment and write its unit.

The magnetic dipole moment of a magnet is the magnitude of the torque that acts on it when it is placed with its axis at right-angles to a uniform magnetic field of unit induction.

SI unit of magnetic dipole moment is NmT^-1.