{"id":5708,"date":"2021-03-12T02:39:22","date_gmt":"2021-03-12T07:39:22","guid":{"rendered":"https:\/\/blogs.sw.siemens.com\/simulating-the-real-world\/?p=5708"},"modified":"2026-03-27T08:59:47","modified_gmt":"2026-03-27T12:59:47","slug":"demystifying-electromagnetics-part-2-wires","status":"publish","type":"post","link":"https:\/\/blogs.sw.siemens.com\/simulating-the-real-world\/2021\/03\/12\/demystifying-electromagnetics-part-2-wires\/","title":{"rendered":"Demystifying Electromagnetics, Part 2 – Wires"},"content":{"rendered":"\n

I Dream of Wires<\/h2>\n\n\n\n

Just as a pipe is a conduit for fluid flow, so a wire is the same for the flow of electric charge. Both flows are considered ‘currents’. Coming in many sizes, but all of similar shape and commonly made of Copper, they allow for the movement of electrons (charge) through them, when forced to do so.<\/p>\n\n\n\n

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Wires come in all sizes, but all have similar shapes<\/figcaption><\/figure><\/div>\n\n\n\n

Where does this force come from and what\u2019s so special about Copper anyway? To answer that, let\u2019s carry on from Part 1<\/a> and look a bit more into the Electric Field.<\/p>\n\n\n\n

From +ve to -ve<\/h2>\n\n\n\n

The electric force field that a charge generates acts in a certain direction. The common notation is that if the charge is +ve (positive) then the force vectors point away from the charge, opposite for when the charge is \u2013ve (negative). So generally the vectors indicate the direction the force would be applied on another +ve charge, were it to be placed in the field.<\/p>\n\n\n\n

What happens if you have a +ve charge point (a deficit of electrons) near a -ve charge point (an excess of electrons)? The 2 force fields combine into a single force field. This combining is known as superposition, electric (and magnetic, potential fluid flow, thermal conduction) fields exhibit superposition behaviour:<\/p>\n\n\n\n

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Electric field superposition simulated by Simcenter MAGNET<\/a> – force field vectors<\/figcaption><\/figure><\/div>\n\n\n\n

Remember the arrows show the direction that the force would be applied to a +ve charge when placed somewhere in that field. The magnitude of this force can be calculated using F=Eq, where E is the field strength (in units V\/m or N\/C) and q is the charge (measured in Coulombs, C). So if a free +ve charge were placed in that field it would \u2018gravitate\u2019 to the \u2013ve charge point (you\u2019ve heard of mixed metaphors, well how\u2019s that for a mixed analogy!).<\/p>\n\n\n\n

When Charges Start to Flow<\/h2>\n\n\n\n

In the above example both point charges sit in vacuum (or air, as air has the same permittivity as vacuum) and the electric field is just one of potential, nothing is actually flowing through it.<\/p>\n\n\n\n

In air though, if the electric field strength is REALLY big (~>3 kV\/mm) it\u2019s strong enough to free up the electrons in the air (ionization) whereupon they start to flow. This is how lightning works. The field strength (Newtons per Coulomb) rips the electrons from the atoms in the air to the extent where it stops being a dielectric and turns into a conductor. A gas, such as Neon under low pressure, ionises at much lower electric field strengths, and that\u2019s how fluorescent lights work. The photons that are produced in both cases are emitted due to side effects of this ripping of the electrons from their happy atomic orbits. <\/p>\n\n\n\n

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Lightning and Neon Lights<\/figcaption><\/figure><\/div>\n\n\n\n

What\u2019s so Special About Copper?<\/h2>\n\n\n\n

A dielectric material is one through which an electric field can permeate, but the charges do not flow. Primarily because all the electrons are happily spinning around, and bound to, their nuclei. A conductor on the other hand is one where there are \u2018free\u2019 electrons that would readily flow, were an electric field to act on them.<\/p>\n\n\n\n

Let\u2019s go back to our 2 charge example and connect them with a copper wire. Think of the +ve and -ve charges as the two terminals of a battery.<\/p>\n\n\n\n

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Electric field force vectors in a Copper wire, simulated with Simcenter MAGNET<\/a><\/figcaption><\/figure><\/div>\n\n\n\n

The Copper not only gathers the electric field and channels it through itself, it then allows its charges to flow. Unlike the point charges floating in air, where the field strength dropped off based on 1\/r2<\/sup>, a conductor (with a homogenous material and constant cross section) maintains the same field strength E (V\/m) throughout its length.<\/p>\n\n\n\n

Wait, what, a constant E field, how does that work? Let’s use analogy again. If you fixed the ends of a metal bar at different temperatures, you get heat flowing down that bar in 1 direction. So long as the bar is all made of the same material and has a constant cross section, the temperature gradient down that bar will be constant, i.e. a constant degC\/m. The point being that the bar channels that heat flow down itself so long as its thermal conductivity is much higher than the effective thermal conductivity of its surroundings<\/em>. Similar for the Copper wire, compared to the electrical permittivity of the surrounding air (or any other dielectric), its effective permittivity is very large, channels the electric field (the ‘permeating charge’) through itself at a constant V\/m, i.e. constant E field*<\/p>\n\n\n\n

(*an overly simplified explanation that doesn’t go nearly deep enough into the physics, but one that I hope will convey the nature of a fixed E field in a conducting wire).<\/em><\/p>\n\n\n\n

Not another mystery?<\/h3>\n\n\n\n

Mystery #3 – The electrons are flowing in the opposite direction to the electric force field vectors<\/p>\n\n\n\n

Maybe more just confusion due to ‘unfortunate’ notation than an actual mystery. A +ve charge is a deficit of electrons. This attracts a \u2013ve charge (an excess of electrons). So the electrons themselves will be attracted to, and will flow towards, the +ve charge point (right to left in the above image). The electric force field notation however is to show the force field vectors moving away from the +ve source charge point. To reconcile this you can think of the deficit of electrons flowing from +ve to \u2013ve are like holes of missing electrons that themselves flow.<\/p>\n\n\n\n

Again, What’s So Special About Copper?<\/h2>\n\n\n\n

Answer: it doesn\u2019t require much electric field force to get its electrons moving<\/strong>. It’s a very good conductor. There\u2019s a single electron in the outer shell of a Copper atom that isn\u2019t so strongly bound to its nucleus, its a ‘free electron’. Give it a slight push and it detaches from its atom and goes with the electric force field generated flow. It has nuclear family commitment issues. The only other metal that is a better conductor is Silver, just a shame there\u2019s not much of that at our disposal and what there is is often wrapped around our fingers or draped around our necks.<\/p>\n\n\n\n

Electric Current is a Flow Rate<\/h2>\n\n\n\n

As mechanical engineers we\u2019re used to the concept of mass flow rate (kg\/s) or heat flow rate (W or J\/s). Electric current is simply a charge flow rate, Coulombs per second (C\/s) defined as Amps (A) and noted as I. A Coulomb remember is -6.24151\u00d71018<\/sup> electrons. So 1A is that many electrons moving through a cross section of a conducting wire every second.<\/p>\n\n\n\n

Consider a free electron in a Copper wire. The force it experiences = Eq<\/strong> (analogous to F=ma)<\/p>\n\n\n\n

The subsequent acceleration the electron with mass me<\/sub> experiences = Force\/Mass = Eq\/me<\/sub><\/strong><\/p>\n\n\n\n

The velocity of the electron at time t after it starts moving = time x acceleration = tEq\/me<\/sub><\/strong><\/p>\n\n\n\n

Take a portion of wire with the constant Electric force field inside it, let loose a free electron, off it goes (OK, OK, as discussed above, consider the blue dot an electron hole):<\/p>\n\n\n\n