What is Magnetic dipole moment: Definition and 59 Discussions
The magnetic moment is the magnetic strength and orientation of a magnet or other object that produces a magnetic field. Examples of objects that have magnetic moments include: loops of electric current (such as electromagnets), permanent magnets, elementary particles (such as electrons), various molecules, and many astronomical objects (such as many planets, some moons, stars, etc).
More precisely, the term magnetic moment normally refers to a system's magnetic dipole moment, the component of the magnetic moment that can be represented by an equivalent magnetic dipole: a magnetic north and south pole separated by a very small distance. The magnetic dipole component is sufficient for small enough magnets or for large enough distances. Higher-order terms (such as the magnetic quadrupole moment) may be needed in addition to the dipole moment for extended objects.
The magnetic dipole moment of an object is readily defined in terms of the torque that object experiences in a given magnetic field. The same applied magnetic field creates larger torques on objects with larger magnetic moments. The strength (and direction) of this torque depends not only on the magnitude of the magnetic moment but also on its orientation relative to the direction of the magnetic field. The magnetic moment may be considered, therefore, to be a vector. The direction of the magnetic moment points from the south to north pole of the magnet (inside the magnet).
The magnetic field of a magnetic dipole is proportional to its magnetic dipole moment. The dipole component of an object's magnetic field is symmetric about the direction of its magnetic dipole moment, and decreases as the inverse cube of the distance from the object.
Consider the following scenario.
We have a closed current loop (say a rectangular loop to make it easier) with magnetic dipole moment ##\vec{\mu}## shown below.
We have a magnetic field ##\vec{B}## which will be defined in different ways below.
I think it is easier to visualize as follows...
These calculations are from these notes from MIT OCW's 8.02 "Electromagnetism", on page 27.
We can represent the location of a point ##P## on the surface of the Earth using spherical coordinates
Let the ##z##-axis be the Earth's rotation axis, and the ##x##-axis passes through the prime...
The following is from Appendix I of these notes from MIT OCW.
Consider a circular loop of radius ##R## lying in the ##xy##-plane and carrying a steady current ##I##.
If we compute the magnetic field at a point ##P## off the axis of symmetry in the ##yz##-plane we arrive at integrals that can...
In the headline to the question the statement should have been:
rotation of macroscopic magnetization = averege (Magnetization current density )
The Magnetization current densities ##\vec{j}_{\text{mag}}^{(i)}## of individual particles ##i## are stationary ##(\vec{\nabla} \cdot...
In my textbook, and on many websites it says that when placed in a magnetic field and then due to Lenz’s law a magnetic dipole moment is created in atoms and so the material gets attracted to the magnet? But then in the case I bring the magnet close to the material very slowly( so the change in...
I'm having a bit of trouble with this exercise because, even if I understand the physics of the dipole-dipole interaction in an ideal classical system, I don't get to know how to approach this problem. I've got a few doubts about how this system would work.
First of all, what would be the...
Hi,
I would like to know why a particle with spin=0 can't posses a magnetic dipole moment?
Using Wigner-Eckart theorem for ##\langle j,1,m,0|j,m \rangle## I get ##\langle j'|| \vec{J}|| j \rangle = \hbar \sqrt{j(j+1)} \delta_{jj'}##
It seems like the right hand side is the magnetic dipole...
According to Chapter 8 of Griffiths' book Introduction to Electrodynamics, the magnetization force that acts on a magnetic dipole is
$$F_M=\nabla (m \cdot B)$$,
where ##m## is the magnetic moment and ##B## is the magnetic field.
For a paramagnetic or diamagnetic particle...
Let's say I have a constant magnetic field and I dive into it a diamagnetic material. Griffiths says that in the presence of a magnetic field, matter becomes magnetized and it will be found to contain many tiny dipoles with a net alignment along some direction.
However, what's exactly the link...
On the first attached page ##\mu_z## is associated with orbital angular momentum (Eq. 41.34). On the following pages (Eq. 41.38) it is associated with spin angular momentum? Are these both part of the same thing? I tried to read further but the book does not address this. In example 41.6 it...
I thought I could replace r^ with z^ and |r|=z since it's only in the z-direction. Is it okay for me to do that?
Also, do I need to consider the magnetic dipole moment, m, only in the z-direction as well? Or can I just keep it as m?
So assuming that I can replace r^ with z^ and keep m as just...
A bar magnet will have a definite magnetic dipole moment, irrespective of the presence of an external field. Why is the moment, then, always defined in relation to the torque it would feel in an external field? Is there any other definition for the same?
Consider the magnetic field B generated by a magnetic dipole. The intensity of B measured along the
axis of the dipole, at a distance of 10 cm from the dipole itself, is 1.0 10-5 T. What is the size of the
magnetic dipole moment? (μ0 =4π10-7 mkg/C2)
a) 0.050 Am2
b) 5 10 -4 Am2
c) 0,1 Am2
d) 1 10...
Homework Statement
This is from Griffith's Introduction to Electrodynamics, where the book is deriving the magnetic dipole moment from multipole expansion of the vector potential
The vector potential of a current loop can be written as
$$\mathbf{A(r)}=\frac{\mu_0 I}{4\pi} \left[ \frac{1}{r}...
Homework Statement
A rotating magnetic dipole is built by two oscillating magnetic dipole moments, one along the y-axis and one along the x-axis. Find the vector potential at a point: (0, 0, ##z_0##) along the z-axis. Then find the magnetic field at ##z_0## . As the magnetic field is a function...
Consider two thin and long, single layered identical solenoids with same DC in them, positioned coaxially. I'm trying to calculate the magnetic force on each solenoid, when there are identical magnetic cores inside them.
As seen in below, I have the general approximation to the force between...
The think is that I would like to create a magnetic trap "minimum of magnetic potential energy in all 3 directions of space" using a distribution of magnetic dipoles as a field generator.
In other words, I would like to know if setting in some way some magnetic dipoles is possible to create a...
Homework Statement
A cylindrical bar magnet whose mass is 0.08 kg, diameter is 1 cm, length is 3 cm, and whose magnetic dipole moment is <5, 0, 0> A · m2 is suspended on a low-friction pivot in a region where external coils apply a magnetic field of <1.4,0,0> T
You rotate the bar magnet...
Im looking to find the resultant magnetic moment of a permanent magnet inside of a steel housing. Some of the remnant flux density is absorbed by the magnet and the field is altered. I want to figure out the total magnetic dipole including the presence of the steel housing. I've been using...
(2)
Hi. I am having a problem with understanding how to approximate 1/R in the forms of equations written above.
I took this equations from a blog, and it tells that I can use talyor polynomial. but I don't get there somehow.
Homework Statement
A 45-m long wire is coiled so that it makes a coil containing 100 circular loops, one on top of the other. If the wire carries a current of 13 A, what is the magnetic dipole moment of the coil?
21 A·m2
6.7 A·m2
3.3 A·m2
2.6 A·m2
1.2 A·m2
Homework Equations
B(z) = u0/2pi...
Homework Statement
Consider a square slab of magnetized material with sides ##2a##, and
thickness ##d##, as shown. The magnetization is not uniform: $$M = M_o cos(\frac{2πx}{
a}) \hat{z} $$b) Calculate the total magnetic moment of this object. How would
you guess the magnetic field decreases...
In one moment in time you have a charge going about in a circle of radius r. in another moment in time the charge goes in the same circle but faster, where Δv is the difference in speed. i want to find the change in the magnetic dipole moment Δm.if magnetic dipole moment m=IA (assuming uniform...
Homework Statement
The Earth's magnetic dipole moment is 8.0 x 1022 A m2.
(a) What is the magnetic field strength on the surface of the Earth at the Earth's north magnetic pole? You can assume that the current loop is deep inside the earth. 6.17e-5 T
(b)How does this compare to 5.0 x...
Homework Statement
The z component of the magnetic dipole moment due to the spin of an electron about its axis is μz = +/- eh/4∏m, where h = 6.63 x 10-34 J s is Planck's constant. A) If μz is parallel to a magnetic field of 10 T, how much energy in electron volts must be supplied to reverse...
imagine a door shaped circuit in the between a south and north pole
such that the long sides are perpendicular to the magnetic field created by the magnet , now
in my physics book , it says that the torque that rotates the door is equal to B * Md where Md is the magnetic dipole moment which...
How they know, how to see the spin of electron>??
Without external field applied, there is random dipole in the paramagnet.
for diamagnet, without external field , there will be no dipole exist.
Thanks.
How to calculate the magnetic dipole moment??
Does anyone out there know how I can calculate the magnetic dipole moment of a simple bar magnet?
Or any kind of magnet?
Without using this formula: \tau = μ x B
Hello, I have this problem. I calculated the dipole energy of a dipole moment in an external field using the equation U_m=\frac{1}{2}\int\vec{A}\vec{J}dr^3=\frac{1}{2} \vec{\mu}.\vec{B} however when the force on a dipole is calculated using \int\vec{J}\times\vec{B}dr^3 the formula...
Homework Statement
I am so stuck on this, and would be very thankful for any help!
a). Calculate the magnetic dipole moment of a single atom, based on the following model: One electron travels at speed 7.40 × 10^6 m/s in a circular orbit of diameter 2 × 10^-10 m.
b). The individual atomic...
Homework Statement
A wire is bent into the shape shown in the figure. The semi-circular part has a radius r = 4.00 cm and the rectangular part has a width w = 1.00 cm. A current of 0.300 A runs through the loop. What is the magnitude of the magnetic moment of the loop?
Note: The figure...
Though this might be absurd, I would seriously like to know the average magnetic dipole of a magnet. For example, you might consider a regular magnet in a remote control car's motors, or any other suggestions too. And I have one more doubt- I know that e.m.f=-d(phi)/dt and phi=integral(B.dS)...
Hi.
So, you surround a ferromagnet with a solenoid.
Run current through solenoid to create B field withing.
2 Questions:
1:Why do the magnetic dipole moments in the ferromagnet "align" with the magnetic field of the solenoid? Doesn't lenz's law say that the magnetic field within the...
I have a Nickel cylinder, 5 micron in diameter and 10 micron in length. I know the external field \vec{B} is 80 gauss, what is the formula for the magnetic dipole moment of this cylinder in the field?
Now I only have the formula for magnetic dipole of spheres, which is \mu = \frac{4}{3}\pi...
Hi,
What direction does the electron's total magnetic dipole moment point relative to it's total angular momentum vector L+S? It seems to me that it would point oppositely to J=L+S since the spin magnetic dipole moment and the orbital magnetic dipole moment are both opposite to L and S, but...
Hello, I have doubts with this problem, I'm not sure, if my solutión is right, so, here we go
Let's two equal charges with the same charge but opposite signs, positive and negative, in a circle, such a distance between them is constant and equal to diametre of the circle. Both charges, turn...
simple magnetic dipole moment with impossible field lines? clueless.
Hello,
I'm taking a first year university course in electromagnetism. At a certain point we came upon the torque on a current loop in a uniform magnetic field. There we introduced the magnetic dipole moment \overline{\mu} =...
Homework Statement
A circular coil having 20 turns and a radius of R = 12.8 cm carries a current of 2.70 A. It is placed in a uniform magnetic field of 60.0 mT. The initial angle between the magnetic moment of the coil μ and the magnetic field B is 26.0o.
1)Calculate the magnetic dipole...
Homework Statement
..Is it possible to find the Magnetic Dipole Moment of a point particle with spin quantum number 2 and mass equal to that of a proton.
I'm not sure how to start this question as there's nothing on it in the textbooks I have!
Thanks
Homework Statement
Assume that an electron of mass m and charge magnitude e moves in a circular orbit of radius r about a nucleus. A uniform magnetic field B is then established perpendicular to the plane of the orbit. Assuming also that the radius of the orbit does not change and that the...
Homework Statement
You have a coil of N turns, with current I through it.
It is in a magnetic field B, which causes it to feel a torque.
Give an expression for its magnetic dipole moment.
Homework Equations
The Attempt at a Solution
Well, I know magnetic dipole moment is A...
Let's say that an electron is moving with constant velocity through a magnetic field. If the magnitude of the field is the same everywhere in space and if it is perpendicular to the velocity of the particle everywhere, the electron will follow a circular path. We all know that. What I need to...
I'm seeking some clarification on a topic found in Jackson 'Classical Electrodynamics' Chapter 5. This deals with the magnetic field of a localised current distribution, where the magnetic vector potential is given by
\vec{A}(\vec{x}) = \frac{\mu_0}{4\pi}...