Physics Lesson 16.5.1 - What is Magnetic Moment? Magnetic Dipole Moment

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Welcome to our Physics lesson on What is Magnetic Moment? Magnetic Dipole Moment, this is the first lesson of our suite of physics lessons covering the topic of Magnetic Dipole Moment, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.

What is Magnetic Moment? Magnetic Dipole Moment

Magnetic moment is a vector quantity that describes magnetic processes. More specifically, it indicates the strength of a magnetic dipole, which represents the relationship between the external magnetic field and the strength of that field itself. Remember, a dipole is the smallest possible magnet obtained when an elementary positive charge (proton) interacts with a negative one (electron).

A magnetic dipole can arise when current flows in circular closed path and since it is a vector, it depends on the direction of the current. This property is used in electrical engineering as a basis for electromagnets, motors or generators.

Generally, there can be two origins for the creation of the magnetic moment:

The first one involves an electric and / or circular current having some current density distribution
The second origin of magnetic moment creation involves particles having their own angular momentum, the so-called spins.

In most cases we are more interested in magnetic dipole moment μ⃗ rather than in magnetic moment m⃗ itself. In simple words, a magnetic dipole moment represents a magnetic north and south pole separated by a small distance.

As discussed in tutorial 16.3 "Magnetic Force on a Current Carrying Wire. Ampere's Force", a torque acts to rotate a current carrying coil placed inside a magnetic field. In this case, the coil behaves like a bar magnet placed inside another magnetic field (as shown in the two figures above). Therefore, we say the current carrying coil acts like a magnetic dipole as it meets the conditions to be as such. In scientific terms, the quantity used to describe the torque of a coil due to the turning effect of magnetic field on this coil is called magnetic dipole moment, μ⃗, as discussed earlier.

The direction of magnetic dipole moment is determined through the same right hand rule used when determining the direction of magnetic field produced by a current carrying wire. This means if we grasp the magnetic dipole moment vector with the right hand so that the thumb shows the direction of magnetic dipole moment, the four fingers show the direction of current.

In addition, the direction of magnetic dipole moment vector is normal to the plane of the loop, as shown in the figure below.

Physics Tutorials: This image provides visual information for the physics tutorial Magnetic Dipole Moment

The equation used to calculate the magnitude of magnetic dipole moment μ produced by a current carrying coil is

μ = N ∙ I ∙ A

where N is the number of turns in the coil, I is the current in the coil and A is the area of the coil. Obviously, the unit of magnetic dipole moment is [A ∙ m₂].

Example 1

A current carrying coil having a resistance of 30 Ω is connected to a circuit supplied by a 12 V battery as shown in the figure.

The diameter of coil is 8 cm. Calculate the magnitude of the magnetic dipole moment produced by the coil.

Solution 1

Clues:

ε = 12 V
R = 30 Ω
d = 8 cm = 0.08 m
N = 5 (number of turns in the coil as seen in the figure)
μ = ?

First, we calculate the current flowing in the coil using the Ohm's Law. We have:

I = ε/R
= 12V/30Ω
= 0.4 A

Second, we calculate the area of coil. We have:

A = π ∙ (d/2)²
= 3.14 ∙ (0.08m/2)²
= 3.14 ∙ 0.0016m²
= 0.005 m²

Now, let's calculate the magnitude of magnetic dipole moment. We have

μ = N ∙ I ∙ A
= 5 ∙ 0.4A ∙ 0.005 m²
= 0.01 A ∙ m²

You have reached the end of Physics lesson 16.5.1 What is Magnetic Moment? Magnetic Dipole Moment. There are 4 lessons in this physics tutorial covering Magnetic Dipole Moment, you can access all the lessons from this tutorial below.

More Magnetic Dipole Moment Lessons and Learning Resources

Magnetism Learning Material
Tutorial ID	Physics Tutorial Title	Revision Notes	Revision Questions
16.5	Magnetic Dipole Moment
Lesson ID	Physics Lesson Title	Lesson	Video Lesson
16.5.1	What is Magnetic Moment? Magnetic Dipole Moment
16.5.2	Torque in Terms of Magnetic Dipole Moment
16.5.3	Energy of a Magnetic Dipole
16.5.4	Work Done on a Magnetic Dipole

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