# How is energy stored in magnetic and electric fields?

We say that there is energy associated with electric and magnetic fields. For example, in the case of an inductor, we give a vague answer saying that an energy of $\frac{1}{2} LI^2$ is stored in the magnetic field around the inductor.

For a capacitor, we say that energy is stored in the field. This is understandable as the electric field is trying to combining the charges on the plates but there exists a physical barrier separating. In other words, I can say that the energy is stored as the electric potential energy of the charges in the two plates.

What does it mean to say that there is energy associated with an inductor's magnetic fields? There aren't magnetic monopoles which are storing magnetic potential energy, but there could be magnetic dipoles which are storing the energy?

Maybe there are photons partying around in the field carrying energy (I am not serious about this comment but I am giving an idea what kind of answer I am expecting).

In my opinion, this is not a duplicate. Answers to similar questions state that work is done by the current moving in the circuit which gets stored in the fields. I understand that. This question asks how the energy is stored in the fields, not where it comes from.

• I'm not sure this is a meaningful question - "how" does anything "store" any form of energy? Sure, a battery has a chemicals in it and we say that energy is stored in the configuration of the chemicals, but "how" do they do that? (What I'm trying to get at is that this is a "bottomless why"-question in disguise. At some point, all physical theories break the potentially eternal cycle of "Why is X like that?" - "Because Y" - "Why is Y like that?"... by saying "that's just the way it is".) Commented Feb 13, 2017 at 14:42
• Duplicate of electronics.stackexchange.com/q/161457/2191 (different Q&A site) which refers to physicsforums.com/threads/energy-stored-in-a-field.74340 which has a nice answer by jtbell Commented Feb 13, 2017 at 14:49
• @RedGrittyBrick That answer explains where the energy comes from, not how it is stored. Maybe my question has no answer as ACuriousMind stated. I went through over 10-15 questions before asking. If there was an answer, someone would have answered it by now. The physics forum answer does help. Commented Feb 13, 2017 at 14:53
• Oops, typo, the electric field is trying to bring them together but it is not able to; therefore there is negative energy associated with it. Fixed. Thanks for pointing out. Commented Feb 13, 2017 at 15:18
• The point is, you shouldn't think of the electrostatic energy being contained in the charged particles. You should think of it as being contained in the field also. Otherwise it gets hard to understand how the electric field from some particles in the sun, that's been traveling for 8 minutes (and thus the original particles have likely changed configuration in the meantime), can deposit energy in the chemicals in your eye to let you see things. Commented Feb 13, 2017 at 16:50

The underlying level of nature is quantum mechanical. The classical concepts, like electric and magnetic fields, rise from this underlying level.

Take a charged capacitor. All the negative charges are on one face and all the positive on the other and there exists a classical electric field between the plates which has energy. This energy is the potential energy which separates the quantum mechanical charges, electrons have been moved from one side to the other and ions were created, and the energy stored comes from this operation.

If one takes an electron by itself, there is a charge, and an electric field associated mathematically with that charge, but there is no energy to be taken or given to the single electron because the charge is intrinsic. Thus the how of ensembles which give electric fields ,ends up to the basic question at the level of a single electron getting the answer "because that is what has been observed".

This always happens with physics because it is a science that uses mathematics to fit observations, and there are basic observations that are assumed. Particle physics has codified them in standard model particle table. So one can answer this question sequentially, peeling the onion of complexity, until one reaches the basic measured facts.

A more complicated argument can be made for the magnetic field, (one has to use the concept of moving charges, an observation) and in the end the answer to the last how will again end in the standard model table.

The separation of charges for capacitors you explained by yourself. I has to explain the storage of energy in inductor coils only.

What does it mean to say that there is energy associated with an inductor's magnetic fields?

Every electron has a magnetic dipole moment This moments in most the materials is equally distributed in space for all the electrons and cancel each other out. (Not so for magnetic materials).

Moving electrons on a curved path inducing a common magnetic field. This happens by the alignment of their magnetic dipole moments. By this the Ohm resistance of a coil is higher as the resistance of a straight wire of the same length. Switching off the current through a coil the electrons alignment gets lost again and a current is induced for a while. (The electrons get disturbed by the thermic movement of the atoms. In ultra old coils this is prevented and the electrons alignment of their magnetic dipole moments is self holding.)

• One is not able to contribute energy from the magnetic field of the inductor. So for example the Lorentz force (moving electrons get deflected under the influence of a magnetic field) does not weaken the magnetic field. Commented Feb 14, 2017 at 6:05