# Inductor's energy

I have some knowledge about LC circuits, like I know Maxwell's equations, the differential equations of circuit oscillator and so on. I am armed with equations to solve physical problems involving inductors and their behavior.

But I always need to understand things as they really are. And I can't find anything on the Internet about how the inductor really works.

So the alternating current in the coil gives rise to a magnetic field in the coil and as I read the energy is stored in it in a magnetic field (but magnetic field cannot do work so I guess it is stored only for split second and it just changes to electric field instantly in a way opposing the current that created this effect and treating the magnetism as the relativistic effect of moving charge which in fact is nothing more how there could be energy stored in it?).

But how exactly does it happen?

So we have LC circuit. We put the electrons on one plate of a inductor. The electrons push the electrons on the other side away creating plus charges and the potential difference which drives the current what in fact makes the capacitor plate be more and more charged, when it is fully charged the current stops.

Now we have also the coil in our circuit. And when the capacitor is fully charged for some reason starts to make current in the other direction (i get that it can be reversed when there is emf and we change its direction but i dont get how it happens only with capacitor and coil). As it does so it moves the electrons through the coil creating magnetic field, which creates electric field in which energy is stored which can be then once more changed into charges moving to the capacitor. And then it repeats.

But how an electron on a microscopic level creates this magnetic field inside the coil, how is energy stored in such inductor, how it gets there, is it stolen from kinetic energy of electron it slows down and gives energy to the coil? How the magnetic field then holds the energy or the electric field that happanes just after? In a static electric field it happens because of plus and minus charges which create the field around but how it happens in that case?

I really lack of good explanation of that process and I can't really think of any electron behavior that would create such effects. Please explain it to me or point me to some readings so I can finally get how it works.

• I see a lot of question marks. I think you have many questions here. Is there a way you could break this down into a few simpler questions? For example, could you ask a question just about how an inductor works by itself, without having to talk about an LC circuit? Or maybe you have a question about how moving charges make magnetic fields? – Brian Moths Apr 24 '14 at 19:31
• I am sorry, my head is messed with that not-understanding of the topic. All questions I asked relate to similar thing. I can't understand how energy stored in capacitor flows to the coil, it is stored there, and then flows back to the capacitor. What actions electrons take so that their energy is stored in that coil? How the energy from the electron is given to the coil and then back to electron so it can carry it to the capacitor? – KabaT Apr 24 '14 at 20:12
• Wow, I see a lot of confusion. So the energy in an indcutor is stored in the magnetic field. And that magnetic field can certainly do work! One way to get the energy out is to hook it up to a capacitor and let the (changing) magnetic field charge up the capacitor. You might want to look up the energy density in electric and magnetic fields. This may help you understand the energy in inductors and capacitors. – George Herold Jul 20 '14 at 13:28

Your "question" contained way too much babble, so I'm only going to answer generally.

You claim to understand Maxwell's equations, so you should be able to see how a inductor works for yourself. When a current flows thru a wire, a magnetic field is created circling around that wire. By wrapping the wire into a coil, the contributions from all the incremental pieces of wire add up to make one larger more concentrated magnetic field.

There is energy in the existance of a magnetic field. Equivalently, it takes energy to build a magnetic field, and you get energy back when you kill the magnetic field. Where did the energy come from in the first place? You already know that current causes the magnetic field. As the field is increased, the inductor will drop some voltage. That voltage times the current is the power that is being put into the magnetic field. Note that this voltage is proportional to the change in the current. A steady current maintains the existing magnetic field, but neither adds energy or removes energy from it.

As for how a R-C circuit works, energy is constantly sloshed back and forth between the inductor and the capacitor. Imagine the capacitor fully charged and no energy in the inductor. That also means the inductor current is zero, which is also the capacitor current since both are connected in series. However, there is a voltage across the cap, which means there is also a voltage across the inductor.

From the circuit point of view, you can think of a inductor as giving inertia to the current. As we saw above, that's not how the physics works, but it can be a useful quick mental model of how a inductor reacts in a circuit. The voltage across the inductor causes current thru it to increase, which moves energy into the magnetic field of the inductor. The current continues to rise proportional to the voltage. The voltage decreases because the current is discharging the cap. This continues until the capacitor is fully discharged (no energy stored in it, voltage across it is 0). At this point all the energy is stored in the inductor and the current is maximum.

The current continues, which continues negatively charging the cap. The voltage building up across the cap is now pushing bacwards against the current. As the voltage builds up, the current decreases ever faster. This continues until the current goes to zero, at which time the capacitor voltage is at its negative maximum. That also means the energy in the inductor is 0 and the energy in the capacitor is maximum. Now the whole process described above repeats with opposite sign.

For a ideal theoretical capacitor and inductor, the energy keeps sloshing back and forth in this way between the capacitor and the inductor forever. Both the voltage and current are sines, but 90° out of phase. The frequency is determined by the inductance and capacitance in a predictable way. In fact this effect is exploited in electronics to filter in or out this resonant frequency. A paralel L-C combination is a useful enough construct to be given its own name, which is a "tank" circuit.

For real parts, there will be some resistance, which you can think of effectively in series with the parts. This resistance will dissipate a fraction of the energy each slosh. The net result is that the voltage and current are sines with a exponentially decaying amplitude envelopes.

• But what happens to the energy of individual electrons in the wires during that process? From where all that energy circulating in a circuit comes from? – KabaT Aug 24 '14 at 7:25
• @Kaba: Charge is different from energy. Charges can have energy relative to what the same charge would have at a different point. The amount of energy per charge is the EMF from the reference point to the charge in question. Therefore asking about "energy of individual electrons" in a circuit without a reference makes no sense. The energy in the resonant tank circuit was initially added to the circuit externally. – Olin Lathrop Aug 24 '14 at 21:27

I assume the first part, up to

But how exactly does it happen?

defines and explains your question, and then you show what you think about it so far?

It looks like the point where it goes wrong is about what the inductor does. There is nothing about "split-second" and relativistic, it behaves in a pretty symmetric way to the capacitor. It's "dynamic" in a way in comparison, but just as the capacitor discharges in a continuous way, the current and the magnetic field increase and decrease in a continuous way in the inductor.

You could review standard intuitive descriptions/introductions of LC circuits with this perspective in mind, hope that will clarify a large part of it.

• I don't understand how precisely energy is stored there. Does vacuum inside gain some energy, or the electrons are excited to higher energetic states? – KabaT Jul 21 '14 at 17:07
• There is a magnetic field inside the coil, which took energy to create, and now can do work; Just the same like the electric field in the capacitor takes energy to create, and can do work, right? Or are you asking on a different level of abstraction? – Volker Siegel Jul 23 '14 at 5:44
• Electric field exists in a capacitor because of charges of opposite signs being located there what creates field between them. What creates the magnetic field in the coil? Spiral movement of charges? Is the energy used to create magnetic field taken grom moving electrons kinetic energy so they slow down or some other way? – KabaT Jul 24 '14 at 5:58