What about electricity? (in atomic level)

A few weeks ago, I told that we don’t need the deeper quantum level mysteries to understand electricity and electronic stuff (i.e) to make things simpler. In case of electric circuits homework, we just use the boring laws of Ohm and Kirchhoff to find out the parameters used inside. Truly speaking, those are not really laws. They’re more an approximation (not to mention that Kirchhoff law was just an upgrade pack to Ohm’s), just like Hooke’s law. They may not always be helpful (say, diode, superconductors, etc.). Okay. Now, I wish to talk about electric currents and voltages in the atomic level…

Atoms & materials…

I don’t have much to say here, hoping you all know that atoms are made of quantum particles. The positively charged proton and uncharged neutron bunched up inside the nucleus with a tremendous force and the electrons with the magnitude of charge equal to that of proton, but negatively charged, move around in the vast space outside the nucleus, the whole set of such objects being considered as atoms that make up “stuff”. That’s far enough.

You may also know that materials conduct when they have free (valence) electrons in their outermost shell and don’t conduct when the shells are completely filled. Yep, that’s right too.

Before sneaking inside, let’s recall the phrase that nature isn’t completely deterministic (at least at the quantum level). Shown on the side, is the quantum mechanical picture of a helium atom (in its ground state). What’s that red & blurry thing surrounding the nucleus? It’s the electron cloud. The particles inside an atom, are quantum in nature. So, we can’t give an exact position and velocity to the electrons. Instead, we compute the chance of finding the electrons at a particular location (the probability) using orbitals (i.e) the patterns of electron density around the nucleus represented by a wave function.

Anyways, the redder the regions, the more likely you ought to find the electrons. I think this picture is enough for us. Electrons, energy levels & orbitals is all we need for today. With this picture, let’s proceed to the different materials.

This was made by a bunch of people who call themselves“vulgarization”.

And, it’d be easier for me if you spend a minute, watching the animation. It’s beautiful, short & intuitive, as it enables us to visualize the difference between conductors and insulators. In an atom, there are discrete energy levels. A solid is a giant collection of a gazillion of atoms arranged in lattices where these energy levels stack up continuously to form energy bands. In metals, the outermost orbital of an atom overlaps with that of the neighboring atoms. In such a case, the valence (outermost) electrons can sometimes be shared with the nearby atoms. Insulators like glass, plastic, etc. have their orbitals filled up completely and so, they can’t give or take electrons from the neighborhood (so do the nearby ones).

Current through a conductor…

Now, current is defined as the rate of flow of electric charges. Meh… anywhere you go, you find the same crappy old definition. It’s right, more or less. But, not much intuitive as it fails to provide any way of looking deeper inside. For now, we’ll stick to the definition and see what really happens inside (having talked so much about materials). Previously, I mentioned that the free electrons in metal atoms (valence electrons, of course) can be shared with the neighboring atoms. The free electrons are redistributed between different atoms so that, at any given time period, the motion of an electron is random & chaotic, which means that there’s no contribution to the current flow. I mean, within that time period, the electron can be stuck with a particular atom, can jump between hundreds of atoms, all kinds of possibilities. Anyways, that’s why we say there’s no net current in a conductor in absence of voltage.

When there’s an applied voltage (potential difference), the motion of free electrons now contribute a tiny part of their motion to the net current in the conductor. This part of motion is what we call drift velocity. It’s worth noting that drift velocity is just a representation of alien particles flowing at around a few mm/s. Electrons don’t move at the drift speed. The speed of an electron is always comparable to the speed of light. It can be around $\mathrm{3\times 10^7\ m/s}$, whereas the drift velocity is only a few $\mathrm{mm/s}$. We see that only one in one trillionth of the speed of electron is contributed to its drift velocity. So, when we speak of drift velocity, we assign the properties of the free electron to some kind of approximated ridiculous charged object which I called alien (just as we use “domains” for studying about magnets, and “grains” for materials, etc.).

So, this drift velocity of the free electrons is what causes current. However, on a conventional basis, we’ve assumed the direction of current to be opposite to that of free electrons. It doesn’t matter anyway. I said, it’s just a plain old convention. Now, here comes the next question. What drives these free electrons?

It’s voltage that’s driving…

There’s an analogy. The voltage is much like pressure which pushes our charged alien particles (we’ve just created them above) inside a conductor. This is not at all wrong. But, it’s not quite. If there’s voltage across the ends of a conductor, current flows inside. Right? Let’s see how. When can we say that there’s a potential difference? For now, let’s go with our everyday helpful source – battery… [*]

When a common lead-acid battery is connected to form a closed circuit, an electron from its negative electrode (as cathodes & anodes mess things up) is dumped into the metal lattice (while another one is sucked inside via the positive electrode). Now, this electron has some energy (the voltage with which the thing is accelerated) so that it travels through the lattice of the metal wire, and repels any free electron on its path. If by chance, this new electron is bound to the outermost orbital of an atom, the other unlucky electron gets out, and it tries to knock some other electron out. It’s not necessarily true that the electron which entered into the lattice, is what goes into the cell again. Nope..!!! It can be a free electron from an atom somewhere in the middle, from an atom near the positive terminal itself, it can be from anywhere else. We can’t say which is which’s… (there’s no absoluteness, that this electron belongs to the 1486th atom, or this electron belongs to the first atom, etc. – That’s just stupid…)

Whatever. Finally, an electron enters the cell and neutralizes the positive ion that was just generated inside the cell as an electron left out (due to some freaky reactions going on inside). Thus, we’ve seen that it’s the interactions between electrons due to a potential difference causes this effect so-called “current”. Okay, now what does voltage represent? I mean, what does it mean to increase voltage? Voltage is nothing but the energy per unit charge (which is the free electron here). The more the voltage, the more the velocity of our alien particles (i.e) drift velocity of our free electrons.

Opposing what created it?

There’s another wonderful interpretation of these horrible things going on inside the “live” wire. When the external field is applied, the free electrons drift to the end where they’re being pulled (attracted) and bunch up. Hence, the other end acquires a positive potential automatically. So, the charges always align themselves in a way such that they generate their own electric field which opposes the field that causes their motion.

Say there are two plates, one having a positive potential, and the other being negative. You place a material in the electric field (say, $E_0$ between the plates. If that’s a conductor, the free electrons move towards the side which is facing the positive plate while the other side facing the negative plate, lacking sufficient electrons, acquires a positive potential. In case of an insulator (which, the figure shows), the electrons can never be able to get redistributed between atoms, as they’re bound strongly to the nucleus. However, the electron cloud can still experience the field and it can shift slightly from the barycenter depending on the field intensity (the same goes to the nucleus). Those +/- tablet-like things you see, indicate the shifted dipoles. In this way, a net potential is generated on the surface of the insulator, though the charges inside seem to cancel out. Ultimately, we conclude that, for metals – the free electrons go bunch up onto the walls whereas for insulators – they get displaced slightly. In both cases, there’s an electric field $E_i$ that acts opposite to the applied electric field $E_0$.

The net electric field is given by $E=E_0-E_i$

If the conductor is perfect in its conduction, the arrangement of the charges is also perfect that they produce an exact copy of the applied field and oppose it, by which the electric field $E$ becomes zero. Hence, the voltage drop across such an ideal thing is zero. Well, in reality, such an arrangement is next to impossible (i.e) there’s always a resistance in the conductor which doesn’t allow such perfection. So, the total electric field $E$ is always positive. This idealism is the basis of a Faraday cage that when an electric field is applied, the charges align themselves to cancel out the field. And since $E$ is so small, we don’t really have to care about that (just approximate it as usual)…

AC & DC?

I used a battery (which supplies direct current) above, because that idea might be helpful almost anywhere in the study of “electricity”. In the case of alternating current, there’s only one difference. Instead of going through the wire like hell, the electrons just oscillate back & forth at some frequency (well, you should’ve seen a sine wave), which is around 50-60 Hz for domestic purposes. A common misinterpretation occurs and a question comes here, “How does alternating current pass through a conductor at all, if the electrons just oscillate?”

The noticeable thing is that the mean position of any free electron in AC is zero. But, that doesn’t mean there’s no power transmission. An oscillation of an electron here, is caused by an oscillating voltage which causes further oscillation elsewhere, etc. Another wonderful thing is that the AC you see here is no different from light or X-rays in a sense that they’re all electromagnetic waves.

Everything has some resistance…

I told you that the free electrons contribute to the current flow via the “drift speed”. While its true for an ideal conductor (as stated above, which has effectively zero resistance), almost all materials in reality, have some resistance to this flow. Or, let’s put it in this easy way. The electron flow, more specifically the electron motion (for the sake of AC) are affected by the interactions of these particles with the atoms in their path. In their rapid motion, they may transfer (entirely based on chance) some of their kinetic energy to the atoms. This leads to the jiggling motion of the atoms, which corresponds to emission of heat. In this way, energy is wasted in the form of heat, which is what’s happening in all materials, except superconductors. In case of superconductors, it’s a wholly different story. There’s some kind of synchronization between the atoms and the passing waves of electrons so that there’s no wastage of energy. But, that’s for another post…

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I also had a thought of discussing about capacitors today (i.e) why it allows AC, but shows infinite resistance to DC, how it stores electrostatic energy, etc. which has been postponed to the next post. Having discussed about these boring concepts of current & voltage today, these would be very helpful for our future posts on electric circuits and electronic stuff…