How can magnetic fields contain energy?

[LarryS]

TL;DR

Magnetic fields cannot do work yet they are said to contain energy ... ?

In classical EM, according to the Lorentz Force Law, a magnetic field can change the direction (momentum) of a moving charged particle but not its energy. Yet magnetic fields like those in solenoids or EM plane waves are said to contain energy. How can this be? What am I not seeing?

Thanks in advance.

 

[AlexB23]

TL;DR Summary: Magnetic fields cannot do work yet they are said to contain energy ... ?

In classical EM, according to the Lorentz Force Law, a magnetic field can change the direction (momentum) of a moving charged particle but not its energy. Yet magnetic fields like those in solenoids or EM plane waves are said to contain energy. How can this be? What am I not seeing?

Thanks in advance.

Good afternoon, bro. Magnetic fields are pretty fascinating, and one of the coolest things about them is that they can actually store energy. At first glance, this might seem a bit counterintuitive as you said - after all, the Lorentz Force Law tells us that magnetic fields can exert forces on moving charges without actually changing their kinetic energy.

But think about it like this: when you flow current through a coil of wire, like a solenoid, you're generating a magnetic field. And that field is actually storing energy, which can be calculated using a mathematical formula, that I am not gonna write down, cos LATEX sucks. This energy is tied up in the magnetic field itself, and it's proportional to the square of the field strength.

Magnetic fields also play a key role in electromagnetic waves, such as light or radio waves. These waves are made up of oscillating electric and magnetic fields that are perpendicular to each other, and they carry energy through space. Interestingly, the energy in these waves is split equally between the electric and magnetic fields.

Now, you might be wondering how magnetic fields actually transfer energy. Well, it's not exactly straightforward. A static magnetic field won't change the kinetic energy of a moving charge, but if the field is changing, that's a different story. Changing magnetic fields can induce electric fields, which can then do work on charges and transfer energy. That is how induction stoves work, how our food heats up in the microwave, or how ice melts when the sun's rays hit the surface.

 

[weirdoguy]

What am I not seeing?

Creating a magnet requires energy. Where do you think it is stored? Or LC circuits, where does the energy of electric filed transfer to when capacitor is losing its charge?

 

[PeroK]

TL;DR Summary: Magnetic fields cannot do work yet they are said to contain energy ... ?

In classical EM, according to the Lorentz Force Law, a magnetic field can change the direction (momentum) of a moving charged particle but not its energy. Yet magnetic fields like those in solenoids or EM plane waves are said to contain energy. How can this be? What am I not seeing?

Thanks in advance.

From a purely logical point of view, all that means is that a magnetic field cannot transfer energy to a charged particle. The field's energy may change in other ways.

 

[Dale]

In classical EM, according to the Lorentz Force Law, a magnetic field can change the direction (momentum) of a moving charged particle but not its energy. Yet magnetic fields like those in solenoids or EM plane waves are said to contain energy. How can this be? What am I not seeing?

Thanks in advance.

Magnetic fields can explicitly and directly do work on magnetized matter.

 

[pines-demon]

Magnetic fields can explicitly and directly do work on magnetized matter.

Made of intrinsic magnetic dipoles.

 

[GravityTim]

At the end of the day, standard thinking is that magnetic fields are fundamental at the magnetic dipole scale. Nobody explains the mechanism there, so nobody can explain the mechanism of the cumulative field either.

 

[GravityTim]

That said, if we consider magnetic flux lines as actual flows of matter, all kinds of degrees of freedom open up.

 

[Dale]

standard thinking is that magnetic fields are fundamental

I would say that the standard thinking is that the electromagnetic field is fundamental. Neither the electric nor the magnetic fields, by themselves, can claim priority over the other. Nor can they be separated from each other in any fundamental way.

 

[Demystifier]

TL;DR Summary: Magnetic fields cannot do work yet they are said to contain energy ... ?

In classical EM, according to the Lorentz Force Law, a magnetic field can change the direction (momentum) of a moving charged particle but not its energy. Yet magnetic fields like those in solenoids or EM plane waves are said to contain energy. How can this be? What am I not seeing?

Thanks in advance.

To understand energy of magnetic fields, it is useful to start from EM waves, which can be understood as an infinite collection of harmonic oscillators. The energy of the electric field corresponds to kinetic energy of the oscillators, while the energy of the magnetic field corresponds to potential energy of the oscillators (to see this, write the electric and magnetic field in terms of EM potentials). The initial claim that magnetic field cannot do work (on point charges) now translates into the claim that potential energy of the oscillators cannot do work on point charges. Only the kinetic energy of the oscillators can do that. However, the potential energy of the oscillators can naturally be transferred into the kinetic energy of the oscillators, which is how the potential energy can eventually produce work in an indirect way.

 

[phyzguy]

In fact, magnetic fields can store huge amounts of energy. Magnetars are neutron stars with enormous magnetic fields, as high as 1E10 Tesla. It is estimated that the total energy stored in the magnetic field around a magnetar is as large as 1E43 Joules. To put this into perspective, that is about as much as energy as the total energy emitted by our sun in a billion years.

A little closer to home, the stored magnetic field energy in a large Tokamak (fusion device) can be as large as 10 GJoules. This would run a 1 kW toaster for more than 3 months.

 

[Dale]

This would run a 1 kW toaster for more than 3 months

That would be one burnt piece of toast

 

[RicoGerogi]

Magnetic fields don’t do work directly, but they still hold energy, given by $$ u_B = \frac{B^2}{2\mu_0} $$. When the field changes, it can create electric fields that do the work, like what happens in inductors. That’s how the energy gets transferred around.

 

[Dale]

Magnetic fields don’t do work directly

They don’t directly do work on free charges. They do directly do work on magnetized material.

 

[pines-demon]

Another important thing is that "holding energy" and "doing work" are not so clearly related... does kinetic motion do work? Does internal energy do work? Does temperature do work?

 

[fluidistic]

Magnetic fields not only contain energy, they also contain angular momentum. If you remove a magnetic field, something has to "absorb" the "invisible" angular momentum, and things that were initially still, can start to rotate. One such example is a magnetized sphere heated above its Curie point. If you have such a sphere hanging by a wire, the sphere will start to spin on itself once it loses its magnetization due to crossing its Curie temperature.

 

[pines-demon]

Magnetic fields not only contain energy, they also contain angular momentum. If you remove a magnetic field, something has to "absorb" the "invisible" angular momentum, and things that were initially still, can start to rotate. One such example is a magnetized sphere heated above its Curie point. If you have such a sphere hanging by a wire, the sphere will start to spin on itself once it loses its magnetization due to crossing its Curie temperature.

This is a neat effect but I thought we were differentiating properties contained in the magnetic field from properties in the magnet. The rotation comes from the relation of the magnetic moments to the spins in the magnet and not from the magnetic field itself.

 

[fluidistic]

This is a neat effect but I thought we were differentiating properties contained in the magnetic field from properties in the magnet. The rotation comes from the relation of the magnetic moments to the spins in the magnet and not from the magnetic field itself.

I think you're right. Essentially the angular momentum isn't stored in the magnetic itself, then, right?
So, if instead of the magnetized sphere we had an electromagnet with some current associated to a B field, if we turn off the current nothing would start to rotate. However, in both cases the dB/dt being non zero, E has to be non zero I think and so S the poynting vector might be non zero and if there are EM waves, there ought to be some angular momentum involved. As far as I know this is also consistent with the photonic point of view, if photons are created during the power off and if they carry angular momentum then it is somewhat involved.