If you’ve ever come across a circuit with a resistor, capacitor, and inductor in series with some sort of complex switching mechanism in between them, and then are asked to graph the voltage or current over time, you’ll know what I’m talking about when I say…
Electricity and magnetism can be a cruel bitch of a course.
I can’t tell you how many forum posts I see like this one:
Or horror stories like this one:
I know when I first took E&M in high school I basically just took whatever equation the teacher wrote on the board, wrote it down, and then went home and plugged in some numbers from my homework problems. Sometimes I got an answer that came out right… but quite honestly I had no real understanding of what was going on going on beneath the surface of the problems that I was doing.
When I got to college it was a similar story with Physics 3 (although electricity and magnetism is typically reserved for Physics 2, there was a pretty big component included in that class for whatever reason). And it was constant battle to get at how to think about electric and magnetic fields, capacitors, and inductors, without reverting back to my plug-and-chug strategy from high school.
It’s hard enough trying to learn something as difficult as physics, but it’s just that much more difficult and frustrating when you can’t even relate what you’re learning to anything tangible in the real world. And I think that’s the biggest problem that we run into we get to Physics 2.
At least in mechanics (Physics 1) you can think, “OK so the roller coaster goes around the loop… this is what tends to happen,” or “if a ball bounces on the ground this is what happens to it,” or “if I have a spinning bicycle wheel then the outer edge moves faster than the inner edge.” We can rely on our intuition that has developed based on things that we’ve experienced in everyday life.
But when we get to talking about electric potential and magnetic fields and interaction between the two things get very murky very fast. Electrons are these beyond-small transient particles that have mass but behave like energy and light.
I mean dear god…
We’re asked to imagine these invisible forces and not only trying to understand what they do but also solve problems with them using complex math.
This is a recipe for disaster, because for a lot of us, applying our standard study routine to this new type of material leads to hours of banging your head against the wall just trying to understand what’s going on, let alone put in the high-quality practice you need in order to prepare for an exam.
And it’s for just this reason that E&M requires an “upgraded” method of thinking to really grip things like: what happens when an electron is traveling through A wire and producing an electric field in a magnetic field simultaneously…
Okay phew… glad I got that off my chest.
So now with our rant out of the way, let’s talk about some actionable practices you can put into play to help “crack the Physics 2 code,” and skip the whole 50% on your first exam part of E&M.
Practice #1: Create vivid analogies to things in the physical world you know well
Now, we mentioned how in mechanics (Physics 1) you can pretty readily rely on your intuition for grasping concepts based entirely on your own personal experience in the physical world. This is AWESOME for learning, because you have a full set of useful analogies ready to go when you need them.
“Analogies are handles to grasp a larger, more slippery idea.”
They’re critical for relating stuff you already know to new stuff that you don’t quite know yet.
Unfortunately, in electricity and magnetism, we don’t have these ready-made analogies, so we have to manufacture them so that we can build up some sort of base “intuition” around each new unfamiliar concept.
For example, let’s take Kirchoff’s Current Law.
It states that the sum of the currents entering a node is equal to the sum of the currents exiting a node. Combined with Kirchoff’s Voltage Law, this also means that more current will always flow towards the path of least resistance.
Now, when you’re just hearing this for the first time it might sound like total gibberish. But then, if we related to something we already know about it becomes a little bit more manageable. So let’s manufacture an analogy…
We can think of the same type of situation looking at a network of rivers.
Photo: Zachary Collier
If you have two small rivers that meet and flow into one large river, the amount of water that passes through those small rivers is going to be the same, in any given minute, as the amount of water that flows through the large river after the two meet.. So this means that in our river situation, the flow rate of the incoming rivers is going to equal the flow rate of the outgoing river.
By going through this exercise we now have a rich visual representation of what’s happening at the electron level when wires meet in a circuit. And the same approximate rules that would apply to the physical form of water will also apply to the flow of electrons.
Now all of this Kirchoff’s Law mumbo jumbo becomes much easier to understand, and we can use this as a reference when we now go to solve circuit analysis problems.
These are the types of analogies that you want to develop for each new concept that comes up in E&M.
Practice #2: Spend a disproportionate amount of time breaking down already solved problems
In addition to relating the new concepts we find in electricity and magnetism to things we already know about, the second thing that we need to do is spend more time doing “deep dives” into problem solving and concepts than we typically would (again, because we can’t rely as much on intuition).
It can be tempting a lot of times to just want to sit down and jump into problems when you’re doing physics… But when it comes to E&M problems, the path to get from the problem the answer is not as obvious. Because of this, you’re going to have to spend a lot more time reviewing solved problems and working your way through each step, understanding what they’re doing to get to the solution, and how that relates to the concepts that are at play.
Exam problem from Koofers.com
This is why I advocate Reverse Learning so much (especially in courses like this) because by working through each individual step and making sure that you understand exactly what’s going on, you aren’t left with any gaps in your understanding and you uncover a lot more about how the different concepts interact to formulate a solution.
Do this type of Reverse Learning practice regularly and you’ll find that you start to develop an intuition for E&M problems naturally, without having to spend a lot of time outside of problem-solving trying to review concepts from your lecture notes, and the textbook.
Practice #3: Make HEAVY use of accurate diagrams
Finally (and this is something that I advocate for all physics problems) you want to spend A LOT of your problem-solving time developing diagrams that label exactly what’s going on in the physics of the problem.
For example, if we’re doing a circuit analysis problem and I’m applying Kirchoff’s Current Law, the first step is to draw out the circuit as accurately as possible, and then analyze each individual node involved in the problem by drawing separate diagrams for each one and labeled in labeling the incoming current and the exiting current.
Once you’ve done this, you can then take what you’ve drawn out, relate it back to the principles that apply (in this case KCL), and then develop your equations based on that understanding. By constructing your problem solutions this way you’ll always have your diagram as a reference point to go back to if you ever get lost or confused.
Alright, so now we’ve got some good tactics here we can use.
Yes, E&M is hard.
Yes, it’s unintuitive.
Yes, we’re talking about spooky invisible forces that we can’t see that are interacting at close to the speed of light…
But if you apply these principles the learning this material you’ll slowly but surely start to develop the same type of intuition that you already have for mechanics problems, and you’ll make it through Physics 2 (relatively) unscathed.