I'm trying to understand the concept but I can't find what I'm looking for. Sorry if I'm wrong at some points as it's the first time I'm studying these stuff.

I understand that when I have an RC circuit the electrons gather at the one plate of the capacitor repelling the next electrons coming , therefore reducing current.Similarly the other plate's positive charge increases creating a potential difference or voltage.This explains to me why current decreases and why voltage increases over time.

Back to inductors now .Let's say we have an RL circuit and I close the switch.The current trying to flow through the inductor will cause a magnetic field around it the direction of which can be found easily with the right-hand rule. The inductor, however, hates change and will try to oppose this change in magnetic flux inducing a voltage.It will be like a battery with the polarity the wrong way.So that is 'why' the voltage is induced. But 'how' is the voltage created because of the change in flux? And how does this voltage progressively get to zero?I know that happens because ΔΦ gets smaller but why doesn't the current stop increasing until the voltage becomes zero?And why does change in flux stop occuring all of a sudden? I'm really trying to find the words here..

  • \$\begingroup\$ You think I can write all this on google? I don't know what to ask. If I ask how is voltage is induced all I get is it's caused by the ΔΦ .And all the videos and sites that pop up explain why it happens and not how. I don't know what to search for. I've been looking into this for 2 hours.That is after I watched read and learnt what I already wrote. \$\endgroup\$ Jan 24, 2017 at 1:26
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    \$\begingroup\$ As a site that's intended to be the goto source for information according to its own set of goals, I'm not sure why many on here are so resistant to achieving that goal. \$\endgroup\$
    – horta
    Jan 24, 2017 at 1:41
  • \$\begingroup\$ en.wikipedia.org/wiki/Faraday%27s_law_of_induction It's called Faraday's Law of Induction \$\endgroup\$ Jan 24, 2017 at 5:43
  • \$\begingroup\$ I know what it's called , I know what happens and why but I want to know 'how' . "Because of Faraday's law" isn't the answer I'm looking for. \$\endgroup\$ Jan 24, 2017 at 7:23
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    \$\begingroup\$ If you want to know why "bottom level stuff" is the way it is, you'll have to ask mother nature. There's nothing it can be derived from. \$\endgroup\$
    – Oskar Skog
    May 8, 2017 at 12:39

5 Answers 5


There is no mechanical explanation for induction. It simply cannot be derived from mechanics. Induction is a phenomena of electric and magnetic fields that have their own laws.

Induction simply states that if a magnetic field changes - no matter, what is the reason, then at the same moment in the same place there unavoidably must be an electric field. This, represented as a 3D vector partial differential equation is one of the famous Maxwell's equations. Those equations (published in 1864) were a summary of more than 50 years long research by several mathematicians and experimental physicians. Nearly all equations had only one reason to be accepted: They produced the same results that were available by doing careful measurements. Induction was one such law. Faraday found it in 1831. About in the same time Henry found it as a side phenomena in electric magnet coils.

One of Maxwell's equations was not based on measurements. Maxwell invented it in his head without getting up behind his writing desk. As a mathematician he had found that his other equations contain a hidden contradiction that other mathematicians probably would soon find and get some good laughs. The new equation would keep the mouths shut. But that's another story, despite the insertion was soon revealed to be the most important invention after Newton's works. The induction had been already well known since 1831.

So-induction exists as soon as magnetic field changes and it shows out as an electric field. Nobody knew and nobody still knows, why, but the electric field was a measurable fact.

Inductive electric field does not need a charge as the starting point of the field. It exists as circle. Those circles are in the changing magnetic field, but perpendicular against it. They are around the changing magnetic field lines just like magnetic field lines are around current.

Electric field puts free electrons to move. How powerful is the motion, it's measured as voltage. How much electrons, it's measured as current. Practical electricians, like us, avoid to think complex 3D vector fields. We are happy if we have less numbers, namely the voltage and the current. Those describe the effect of the fields in electronic parts and wires. The total structure of the fields most often is not interesting.

Think about an electric magnet. It's a wire with electric current. The wire is twisted to be a coil to intensify the magnetic field locally. For even more effect, some iron is inserted to the field. The higher is the current, the more intensive is the magnetic field. That's why by breaking or increasing the current we can easily change the magnetic field.

The induction in those cases generates immediately the electric field. That's perpendicular with the magnetic field and thus pushes electrons in our coil's metal along the wire's direction. That we see as the induced voltage.

How to utilize the effect as directly and observably as possible? One story: I was some years teaching in an institute of adult education. Electricity elementaries was one of my duties. Induction was especially difficult for most of those students. The general goal in their studies was to create professionals for tasks in the field of violence. These guys specialized to electronic equipment - how to use and maintain them.

Those guys had a good practice to learn and remember via their muscles. So I built a muscle memory utilizer for the supplementary induction studies. It was the following:

enter image description here

Warning: Today it's strictly forbidden to apply devices like this on people or animals without an official permission and having officially approved equipment. Don't do this yourself! Why? If somebody gets injured or only lets on about the method, you will be in a serious trouble. In old times it was only humour.

The student who had shown a need of supplementary lessons, took the terminals into his hands. The teacher estimated the wanted depth of the lesson and turned the wire pot respectively.The button was pressed and released. It really was very obvious that the amount of the learning increased at lightning speed.

Sometimes the teacher reiterated the lesson several times before the student had absorbed enough the new knowledge to be available to release the terminals.

The battery voltage was 4,5 V and the 5 Henry coil had 150 Ohm internal resistance => the maximum available lesson depth was only 30 milliamperes.

How this works? When the button is pressed, the coil current grows in the beginning at rate 9V/5H ie. growth rate is 1,8 A per second. The current is not able to grow very high. The growth slows down nearly instantly and the final coil current is determined by the total resistance and the battery voltage. In this case the maximum coil DC current is about 30 mA, when the pot is at zero Ohm (= max depth)

When the button is released, the coil current does not break. The induction generates all needed extra voltage onto the terminals that current can continue to flow. The current goes through the easiest way and in this case it is the student. If there's none then somewhere clicks a spark. The voltage jumps as high as is needed to find a way.

Current through resistive material generates heat and that eats the energy of the magnetic field rapidly. In practice the lesson lasted usually well below one millisecond. Thus several reiterations were possible without a bad delay for the schedule.

  • \$\begingroup\$ I remember our physics teacher doing exactly this to one of the lesser academic kids at school. The funniest part was, he explained exactly what was going to happen before it did, but of course the poor kid was too busy grinning at his mates to bother listening to a word, so it came as a shock to him! \$\endgroup\$
    – Echelon
    Sep 21, 2018 at 22:39

It's more like, if you put a voltage on an inductor, magnetic fields can't be changed instantaneously so current won't flow according to ohms law to begin with. The magnetic field will grow eventually along with current until it reaches steady state according to the voltage and ohms law.

Then when you open the switch, a voltage gets induced because you have a magnetic field that begins collapsing. Now you have nowhere for the current to go even though this magnetic field collapsing is causing a severe amount of "pressure" (aka voltage) to be generated. Once the electrons find some leakage path the voltage will come back down, the magnetic field will weaken, and you'll be back to a standard open circuit without a magnetic field.

  • \$\begingroup\$ So it's basically like inertia I guess. But if you have just an R circuit the current obeys Ohm's Law immediately. In this case though the magnetic field can't be produced that fast and that's the reason things happen slowly.That really helps my understanding but I'm still I'm trying to figure out how the magnetic field led to the creation of voltage.Maybe the answer I'm looking for lies in molecular level. \$\endgroup\$ Jan 24, 2017 at 1:39
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    \$\begingroup\$ @JohnKatsantas i'm not sure anyone really knows the answer to your question. The reason for this is that I believe all of these related items are scientific Laws. Laws don't have an explanation yet. They just are. Kind of like the law of gravity. We don't know why it happens. We just know we can certainly observe its events and it happens every time. Maxwell, Faraday and Lenz's law cover this topic and the surrounding understanding. \$\endgroup\$
    – horta
    Jan 24, 2017 at 1:43
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    \$\begingroup\$ I was worried it might have been one of those cases. At least someone told me and I can stop looking for it now and study the rest I have for my test. Thanks! \$\endgroup\$ Jan 24, 2017 at 1:47
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    \$\begingroup\$ @JohnKatsantas No problem. And to confirm your previous comment, yes indeed, it is very much like inertia. I usually visualize it as water running through a pipe. If you shut the valve off quickly you'll get water hammer. The exactly equivalent effect on a physical/hydraulic level: en.wikipedia.org/wiki/Water_hammer \$\endgroup\$
    – horta
    Jan 24, 2017 at 1:49

Here is an example circuit in the free simulation environment SystemVision Cloud: https://www.systemvision.com/design/simple-rl-magnetics

enter image description here

It shows an exploded view of the magnetic circuit of an inductor, where flux and MMF interact between the winding and the magnetic core. The "probes" can be moved around to look at any signal in the circuit, including not just voltages and currents, but also power dissipation in the resistor, flux density (b) and energy stored in the core, etc.

You'll see that as current increases in the winding, the winding MMF increases directly in proportion to it (i.e. i * number of turns). The default core model is linear, so that flux is directly proportional to the MMF applied across it. But as the flux increases, there is a back-EMF voltage that is proportional to the time-derivative of this flux. That voltage is opposed to the externally applied voltage, so there is initially only a small voltage drop across the external resistor, even though the voltage source applied a pulse of +5V. That is, the back-EMF voltage of the winding is initially almost 5V also, because the flux is increasing rapidly initially (highest di/dt value).

A "live" picture is worth 1000+ words, so play around with this yourself. One really interesting thing to look at, in my opinion, is to plot the power output from the source compared to the power dissipated in the resistor. Note that when the voltage source goes back to 0.0V, and of course its power output also goes to 0.0W, the resistor power does not go to 0.0W! This is because the energy that was stored in the magnetic core is converted back to electrical power (winding v*i /= 0.0), to continue to supply the resistor with power, temporarily.


If you already grok capacitors, then you can apply all of that knowledge to inductors, as long as you make a few changes to some of the things you know and love.

What's the same? Capacitors and inductors both store energy, in a field. A change in stored energy means power, to change it quickly means a lot of power. That's where they both get the ability to do unexpected things at their terminals.

What's different? Capacitors and inductors are duals. That means for voltage, use current and vice versa, for series use parallel, for short use open etc.

1a) Consider we charge a capacitor from an initial 0v from a current source. The voltage rises as charge, the current*time, flows in. If the current source is actually a voltage source in series with a resistor, then the charging current falls over time, until there is no voltage across the resistor, and the capacitor has the same voltage as the source.

1b) Now open circuit the capacitor. The terminal voltage is initially unchanged. Any shunt conductance across the plates due to leaky dielectric will reduce the voltage over time, by setting up a current that will reduce the stored charge. For most capacitors, the time constant for this can be measured in minutes to days. This loss mechanism is not a fundamental part of the capacitance, and can theoretically be zero.

1c) Now short circuit the capacitor. A potentially very large current flows, as the capacitor 'tries' to keep the terminal voltage the same. The current is limited only by the residual resistance of the external circuit.

2a) Now consider charging an inductor from an initial current of zero from a voltage source. The current rises as flux, the voltage*time, flows in. If the voltage source is really a current source in parallel with a resistor, then the charging voltage falls over time, until there is no current through the shunt resistor, and the inductor has the same current as the current source.

2b) Now short circuit the inductor. The current through it is initially unchanged. Any series resistance in the copper wire will reduce the current over time, by setting up a voltage drop across it due to the circulating current. For most inductors, the time constant for this can be measured in uS to seconds. This loss mechanism is not a fundamental part of the inductance, and can theoretically be zero, and actually is zero in superconductors.

2c) Now open circuit the inductor. A potentially very high voltage builds as the inductor 'tries' to keep the terminal current the same. The voltage is limited only by the residual conductance between the terminals.

So I've run through two dual scenarios, that are exactly identical when we swap volts for current and so on. So there is no fundamental reason why inductors should be any less understood than capacitors.

... however ...

a) Capacitor self time constants, because of the very insulating dielectrics we have available, are long enough to do reasonable experiments with. We understand the charge stays put.

Inductor self time constants, because even the best conductor we have at room temperature is still very resistive, are so short we tend to overlook the behaviour. We think the flux disappears, we don't feel that it too tends to persist like capacitor charge.

b) Capacitors feel like voltage sources, inductors feel like current sources. We grok voltage sources, a lead acid battery is a very good voltage source, an AA battery is a reasonable one. There aren't any current sources easily to hand, we are not familiar with them at all.

  • \$\begingroup\$ A shorted solar panel behaves like a current source. \$\endgroup\$
    – user253751
    Dec 7, 2017 at 0:30

You could think of the inductor as a tightly wound water slide. The water source is backed up behind a valve and when it's released it doesn't just nicely flow through. It'll smash into the first bend it sees and the equal and opposite reaction will be to push back. After that it'll work itself out and eventually play nice.

The actual theory is all well and good but you'll forget it and all you'll be left with is water analogies until you re-learn the theory.

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    \$\begingroup\$ It's more like a big heavy waterwheel that blocks the whole stream. Water can't get past until it pushes the waterwheel up to speed. Then if you try to stop sending water, the wheel will keep pulling all the remaining water to the other side until it's slowed down. \$\endgroup\$
    – user253751
    Dec 7, 2017 at 0:35

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