How does alternating current even work if the charges never go anywhere? The answer to this question rearranged all my intuitions about circuits. Prepare for a mind blow.
This episode was made possible by generous supporters on Patreon. Hey Crazies. One thing you cannot do is confuse the motion of charge with the motion of energy.
They are not the same thing. Let’s define them both very carefully. Electric current, or just current for short, is the flow of positive charge.
Wait wait, positive charge? Yeah, you can thank Ben Franklin for that. To the timeline!
! Back in 1748, Ben Franklin stated two things about electricity. One: Amber becomes negative when rubbed.
And Two: Current is flow of positive charge. Then, 150 years later, JJ Thomson discovered the electron and we realized we had a problem. You’d think we’d have adjusted one of Franklin’s definitions, but we didn’t.
We doubled-down on them instead. Even though we know negative charge is what moves in a current, we pretend like it’s positive charge moving in the opposite direction. Human stubbornness will never cease to amaze me.
Anyway, we have to live with it now. Electric current is the flow of positive charge and we measure it in amperes, or amps for short. The energy flow, on the other hand, is best described by something like power.
That’s basically how fast the energy is being used and it’s measured in joules per second or watts. Turn down for watt! Anyway, current and power are related to each other.
Since current is charge over time and voltage is energy per charge power is just current times voltage. It’s a relatively easy calculation. But our original question isn’t really about amounts.
It’s about direction. This equation tells us nothing about direction. But isn’t the energy carried along by charged particles?
Won’t the current and power be the same direction? Well, “yes” to the first question, but “no” to the second. The charged particles do have energy because, well, everything has energy, but that’s not the energy that's powering whatever device you’re using.
Let’s say, for the sake of simplicity, it’s just an incandescent light bulb. What I’m about to explain will be true of everything, but we don’t want to get caught up in unimportant details. On that same note, let’s power that light bulb using a simple battery.
The positive end has a higher energy than the negative end so, if you give the charges a path, they’ll fall to the lower energy. That’s what an electric current is. Over time, we know the energy in the battery goes down as we use our devices.
It can cause sheer panic when it’s the battery in our phones, but this same thing happens with the light bulb too. The energy in the battery goes down as the light bulb emits heat and light. The flow of that energy is described by something called the Poynting Vector.
No, that’s not a typo. It’s named after John Henry Poynting, the guy who came up with it. It is a pun though because it points in the direction of energy flow.
I love puns. Anyway, here’s the Poynting vector. E is the electric field, B is the magnetic field, and mu is just a constant to make the units come out right.
Don’t worry too much about it. That gives us the energy flowing through an area every second. A common example of this vector is light.
Light is an electromagnetic wave, a disturbance in electric and magnetic fields that results in a flow of energy. From a bulb, that’s looks something like this. But the Poynting vector is true for any electric and magnetic fields, not just the ones you find in light.
What’s the deal with those fields again? Hmm, I guess I can do a quickie review. Charges affect the electric field and moving charges affect the magnetic field.
These fields are not attached to the charge. They stay attached to space, while the charge moves. If no charges are around, the fields are still there.
They’re just zero. A similar thing happens around a battery. This battery can be thought of as two equal but opposite charges.
Those charges will affect the electric field. But, according to the Poynting vector, we don’t get an energy flow without also having a magnetic field. The battery isn’t going to lose energy just sitting there.
It has to be connected to something. Here’s the electric field around the battery again, drawn a little simpler. If we connect some wires and a light bulb, the field will distort a little.
Even though the charge in that extra stuff is balanced, it still channels the field through itself. The field in those materials is strong enough to push charge along. Now that there’s a closed loop, the electric field will cause a steady current and, where there’s moving charge, there’s a magnetic field.
So now we have an electric field and a magnetic field. According to the Poynting vector, we get an energy flow. But this cross product means the flow has to be perpendicular to both fields.
The flow of charge is the same direction as the electric field, which can’t be the same as the flow of energy. According to Poynting, the energy cannot flow in the same direction as the charge. Wait, what?
! Exactly! When I realized this, it broke all my intuitions about circuits, but here’s what everything looked like when I put it all back together.
If we zoom in one of the wires a little, we’ve got a strong electric field inside moving the current along and a little electric field outside. We also have a magnetic field inside and outside. Using the Poynting vector, we get an energy flow toward the center of the wire.
The energy comes from the field outside the wire! Wait! Didn’t you say earlier the energy comes from the battery?
Yeah, but it happens indirectly. Inside the battery, the electric field points the opposite way, but the magnetic field points the same way. If we look at the battery the same way we did the wire, the energy flows out of the battery and into the field.
So the energy the wires and the light bulb gain from the field is the same amount of energy the battery loses to the field. The energy flow in this circuit looks like this. It’s cray cray!
It doesn’t even matter if it’s AC or DC. With alternating current, or AC, the current just moves back and forth because the electric field keeps switching direction, but so does the magnetic field. If this changes direction and so does this, the two effects cancel.
The energy flow maintains its direction. Even in an AC circuit, the energy flow is out of the source and into the devices. How can that possibly be?
Aren’t AC generators, like, miles away? Yeah, but that’s totally fine. Remember these fields are everywhere and affected by all charges everywhere.
The energy coming out of a power source doesn’t have to be the same energy going into your devices. Conservation of energy just says they have to be the same amount. If you calculate the amount of energy flow across the surface of this wire.
You will get exactly what we’d expect for the power lost to heat and light. So how does the energy actually flow in a circuit? The energy that makes a circuit work comes from the fields around it.
A source of energy like a battery just replenishes what gets used and all the electric current does is provide the mechanism we need to make the energy flow. So, are you as mind blown as me right now? Please share in the comments.
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The featured comment comes from “space is where we belong to! ” who asked: Is wind just a little nudge to get the coil spinning? No no, we’re not creating perpetual motion machines.
The induced current actually resists the motion of the coil. Without the continued push from the wind, the coil almost immediately stops. Anyway, thanks for watching.
