Please explain Maxwell's equations

Yes, first define the variables.

Perhaps skip to the part where you explain what is being described. Then describe the math.

That’d be good enough. I have the darndest trouble with this one :rolleyes:

That’s because you can’t skip the math. Electrodynamics is all interacting fields and charges, and you need the mathematics (specifically, vector calculus and partial differential equations) to describe me. You can no more comprehensibly describe the interaction of Maxwell’s equations and the Lorentz force in English than you could describe a symphony.


Yes, but you can write a symphony on a piece of paper, and although someone unversed in the language of music wouldn’t be able to make head nor tail of it, once it was played or performed, it would make perfect sense to the listener. You do not need to understand musical language to appreciate it.

Maths seems to be different. If you haven’t got that geek gene that makes thinking in numbers feel natural, and sensible, without a practical demonstration of some sort, it all just comes across as abstract bollox.

If something can only be understood by other mathematical geniuses and cannot be explained in words, what use is it anyway?

E (or D) is the electric field, B (or H) is the magnetic field, rho is the charge density, J is the electric current density. The equations determine the E and B fields for every point in space given some configuration of charges and currents.

That describes a lot of modern physics, without which you wouldn’t have a computer to read these posts on.

What ever equations and mathematical jiggery-pokery went into making this computer, surely it had to be translated into English or some other language, to make the physical components?

Nonsense. Very, very few people–and I’m talking in terms of a few hundred or less–have any “geek gene that makes thinking in numbers feel natural,” or similar natural intuition about advanced mathematics. The majority of us have simply spent the time–and it is just time, sweat, and tears–to be able to grind through the math, the same way a trumpet player learns to play the notes, or a dancer learns steps and turns.

Electrodynamics is all math, and despite attempts at analogies to water flow and such, it just isn’t an intuitive science. You crank through problems over and over until you get a sense for how things should work, and that is as close to intuition as it gets. Simplicio’s post, as sparse as it is, is about the most useful explanation in plain English. You can use more words, a lot of words, to describe specific electrical and magnetic phenomena, but if you want to understand Maxwell’s equations you have to use math.


To the OP’s request, I want to note that a full understanding of electricity and magnetism, including Maxwell’s Equations, is really pretty much inextricable from math. In fact, when doing E&M calculations, it’s often easy to forget that there’s real-world physics involved, and to get caught up in the math. Very often exercises in electromagnetic fields feel like exercises in differential equations and infinite series.
That said, it’s not impossible to get an explanation and a feel for what’s going on. Isaac Asimov published a series of books on physics for the general reader that didn’t require math, under the collective title Understanding physics. I’m happy to see that they are back in print, collected in a single volume, which I highly recommend:
Note, as well, that Maxwell’s equations are EM in highly condensed form. You can pick up a lot of this via the internet by googling topics such as Ampere’s Law.ère’s_circuital_law
In cgs units in differential form (as one of Maxwell’s equations) it looks formidable and daunting, filled with unknown cabalistic signs. But it can be presented via the special case of a single straight wire carrying a current with almost no math.
If you’re more ambitious, you can go one from Asimov to undergrad texts like the Schaum’s Out;line series, or Purcell’s book in the Berkeley Physics Series (if that’s still in print)

I think the first reply may have derailed this thread. The OP does not appear to be asking for the math to be skipped.

Bolding added.

In simple English:

  1. Gauss’s law. Electric charges create electric fields where the strength of the field is determined by the distance from the charge.

  2. Gauss’s law of Magentism. There are no Magnetic Monopoles - the magentic field flux through any Gaussian surface sums to zero.

  3. Faraday’s Law. A change in magnetic field strength induces a change in electric field strength.

  4. Ampere’s Law plus correction. Faraday’s Law reversed, plus electric current also creates magnetic fields.

However, you’re asking more about what exactly the math parts mean. Well, they basically describe the magnitude and direction of all the changes that occur in the above. You really can’t boil it down much further than that without working directly with the differential equations. However, given that I’ve not actually worked with the equations myself, I can’t personally do any better.

And that’s precisely what my suggestion attends to.

Eh, I’ll give it a shot:

The equations deal with electric fields, and magnetic fields, and how they interact.

It turns out that if an electric field is changing (increasing or decreasing) that creates a magnetic field. The converse is also true: A changing magnetic field creates an electric field.

So if you have a changing magnetic field, this creates a changing electric field, which creates another changing magnetic field, which…you get the idea.

So the equations describe this interaction, and account for the propagation of EM waves…light, radio, and like such.

Note that the created fields are due to a change in the “source” field. For this reason the equations are “differential equations”. An “ordinary” equation would describe how X depends on Y for example. A differential equation describes how X depends on the rate of change of Y. To go beyond that is normally the subject of 4th, 5th, and 6th semesters of a college level calculus sequence of classes.

It is only a slight joke to say that the best way to solve a differential equation is to already know the answer.

ETA, yes I know MEs are PDE’s figured that is beyond the scope of the OP.

These days, not necessarily–since a lot of this kind of production is computerized and automated. Instructions may never have been written down in English! Some components may have been made in a way such that every human involved used only math and logical formalisms!

But even barring that possibility, supposing there had to be explicit English instructions for making each component, those English instructions couldn’t have been created without the incomprehensible-to-you-and-me math having been done beforehand.

Last year, when I was doing physics homework people would often ask whether I was doing math, and vice versa for math homework.

OP, try this link:

Chinese seems to be different. If you haven’t got that geek gene that makes thinking in ideographs feel natural, and sensible, without a practical demonstration of some sort, it all just comes across as abstract bollox.

If something can only be understood by other linguistic geniuses and cannot be explained in words, what use is it anyway?

That’s exactly the same as what you wrote, and it’s obvious nonsense. The problem is you, not math.

You want to understand Electricity and Magnetism without the math? Then check out these awesome video lectures from MIT: Walter Lewin E/M Lectures

It’s the lectures from the actual class. He does write some math on the board, but you don’t need to understand it. He illustrates all the principles through examples and demonstrations which will give you the gist of how it all works.

Requirements and specifications for design, production, and testing are in English (or some other natural language), but the information on how to actually construct, say, a VLSI chip are almost entirely in some kind of numerical code (CAD models, SPICE code, EM interaction models, et cetera). There is no way you could describe every circuit element and function in English and have anything usable. You’ve have a detail product description that would fill a warehouse, and it still wouldn’t be useful.

Let me put it in a slightly less abstract example from my experience. When you design a mission for deploying a payload via a space launch vehicle (rocket), you have to write flight software to control the vehicle. This software takes a large number of parameters and data, such as: nominal trajectory and allowable variances; expected and derived thrust curves for each motor/engine; aerodynamic loads and losses with respect to altitude, speed, and angle of attack; expected wind shear based upon atmospheric models; physical characterization of the TVC and ACS systems; bending modes and dynamic response of the rocket body and payload; and so forth. The software inputs and requirements are described in English at a general level, but the specific inputs are are all mathematical models that are provided to the code either as inputs or hardcoded in as algorithms, and are never described in detail in natural language. So, for example, there may be a requirement that it be within a flight envelope at such and such altitude and azimuth and achieve an nominal orbit of X km by Y km with a variance of eccentricity of Z, but all the details that feed into the flight code that tells the avionics how to steer and throttle the vehicle are never described in English except in the most general terms, and not in any way that would let you reproduce or replace the flight code from scratch.

The labels provided by glowacks are just that. The don’t really describe what the equations do, except in the most general terms, which don’t mean anything if you don’t understand the interactions between Maxwell’s equations. And therein lies the beauty of Maxwell’s equations; the fact that while they are four distinct equations, they are cojoined such that, combined with the Lorentz force, they describe the effect of electromagnetic fields upon electrically charged particles and magnetic fields. You can’t describe the equations in isolation of each other; you have to see how one influences the others, and the only way to do that is by actually applying them to problems and doing the math. Any amount of verbiage “describing” the interactions is just a lot of technobabble until you can actually see how the math works. Some very, very smart people may have a knack for visualizing the working of EM fields, but for most of us we have to muddle through the equations again, and again, and again, until we get familiar enough to say, “div B through closed surface S gives the magnetic flux, blah blah blah” and actually have it mean anything. It’s just like learning a new language structure, except one that describes exotic fruits that you’ve never seen or tasted.


Thanks guys. This is why I keep coming back to the 'dope :slight_smile:

I’m not afraid of the math- I minored in it- but it looks like my diffy-Q is worse than my google-fu. I wanted to start over in attempting to understand Maxwell’s equations, and so wanted to start with the English explanation.

Maybe someone would like to provide some examples to practice running through the equations?

Of course if those equations and software are written without regard to units, your rocket might flip over and crash into the ground since the flight software is expecting the azimuth rate to be in Horses per Submarine rather than degrees per second or whatever units you have chosen.

I think Beagle 2 is buried in a Martian mountain somewhere for just that reason.

No, that was NASA’s Mars Climate Orbiter.

Cal’s Schaum’s Outline suggestion should cover that.