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Hey Crazies.
I’ve made a particular statement many times on this channel.
Light is an electromagnetic wave, a disturbance in electric and magnetic fields.
Which begs the question:
Huh? What does that even mean?
Well, let’s start from the beginning.
No no no, stop that!
We’ve talked about this!
Stupid AI.
I mean from the beginning of our most recent series on electrodynamics.
Whenever it’s possible, we treat the electric and magnetic stuff separately.
If there’s a charge, there’s an electric field.
If that charge is moving, there’s also a magnetic field.
That’s two separate fields:
The electric field and the magnetic field.
And people spent the majority of the 1800s trying to describe how they work.
To the timeline!
In 1835, Gauss’s law showed us electric fields came from charges.
In 1820, Ampere’s law showed us magnetic fields came from moving charges.
Both confirming what we covered earlier.
Bingo Bango! Mystery solved. Fields described.
End of story.
Wait a minute!
That can’t be the whole story, right?
I mean, we’ve seen other laws in this series.
There was a Gauss’s law for magnetism too and, in 1831, we got something called Faraday’s law.
That brings the equation count up to four.
Each of these laws says something about at least one of these fields.
Gauss’s law for electricity says electric fields point away from positive charges and toward negative charges.
Gauss’s law for magnetism says magnetic fields always form closed loops.
Ampere’s law says those closed loops wrap around moving charge.
Faraday’s law is the odd one out on this list.
It seems to connect the fields to each other.
Basically, a changing magnetic field makes an electric field.
Wait wait wait.
One of the fields can make the other field?
Yeah. It’s pretty weird, isn't it?
Come to think of it, this is kind of big deal.
If one field can make the other field, then maybe charges don’t make the fields at all.
Maybe they just affect them.
Maybe they’re a thing all by themselves.
I mean, we said light was a disturbance in electric and magnetic fields
and light is a thing all by itself.
So it makes sense.
In fact, that’s exactly how we imagine fields these days.
Notice the arrows in this graphic remain in the same place as the charge moves.
They’re attached to the space, not the charge.
If there aren’t any charges around, we like to imagine the fields are still there
and just have a value of zero.
We wouldn’t really get confirmation of this though until the 1860s.
Back to the timeline!
Thirty years after Faraday, James Clerk Maxwell enters the conversation.
He thought to himself:
If a changing magnetic field can affect the electric field,
it would be nice if a changing electric field could affect the magnetic field.
Yes, they should be able to affect each other!
So he took Ampere’s law and tacked on an extra term to make it happen.
Did he just invent it out of thin air?
No, not really. I’m lying a little bit.
He wasn’t so haphazard about it.
He did imagine a conceptual model first, with a sea of tiny molecular vortices.
That model was horribly wrong, but his result turned out to be correct anyway.
That lucky son of a [beep].
Anyway, Faraday said a changing magnetic field gives us an electric field
and now Maxwell's said a changing electric field gives us a magnetic field.
The circle is now complete.
This discovery had profound consequences for our understanding of these two fields,
but Maxwell kind of fell short in this department.
His versions of the equations were kind of a mess.
There were literally 20 of them.
With some vector calculus, we can combine some to shorten the list to 8,
which makes Ampere’s law a little more obvious, but Maxwell wasn’t interested in being concise.
He was an experimentalist and wasn’t super great at deep truths.
It wouldn’t be until Oliver Heaviside arrived 20 years later,
that we actually get the equations everyone knows.
And, yet somehow, these are called Maxwell’s equations.
History is cold-hearted monster.
Anyway, the point is, we’ve described a way for these two fields to affect each other.
Back to the timeline!
Maxwell thought about this connection for a few more years
then, suddenly, something occurred to him:
If a charge with a velocity gives us a magnetic field,
then a charge with a changing velocity should give us a changing magnetic field.
That’s when Maxwell saw the light!
Like, literally. He rediscovered light.
We know from Faraday a changing magnetic field gives us an electric field.
If that electric field is also changing, then we get a magnetic field,
a changing magnetic field.
Which gives us a changing electric field,
that gives us a changing magnetic field,
that gives us a...
You get the point!
Maxwell had discovered electromagnetic waves and, when he calculated the speed of those waves,
he found it to be a constant
299,792,458 meters per second: the speed of light.
And it’s not just about light.
That’s the speed at which any change happening with the charge can be communicated to the field.
There’s a delay between when the charge moves
and how the field responds at all of these points in space.
It’s difficult to see in this graphic though because everything is happening so fast.
We need to zoom way out and slow the speed of light way down to get a better view.
Let’s imagine a radio transmission tower.
Inside the tower, charges move up and down.
Since that’s a type of acceleration, the magnetic field is changing over time.
The field arrows nearby respond almost immediately,
but the ones farther away don’t respond until later.
The speed of light demands that there be a delay.
In a way, the distant field arrows are responding to where the charge was in the past
and what it was doing back then, rather where it is and what it’s doing now.
The result is a wave pattern, which we usually write using sines or cosines.
We just evaluate each arrow in the field at an earlier time
depending on how far away it is from the source.
That’s why we get this extra term.
But, math aside, let’s just stop and appreciate something for a few seconds.
This field disturbance is self-sustaining.
You can stop the charge from moving and the fields will continue to do this.
There’s now a disturbance in a couple fields that travels out through space.
All because a charge once accelerated at some point in the past.
And that field disturbance is what we call light.
So, have you seen the light?
Let us know in the comments.
Thanks for liking and sharing this video.
Don’t forget to subscribe if you’d like to keep up with us.
And until next time, remember, it’s OK to be a little crazy.
Several of you asked about the James Webb Space Telescope in the comments.
Yes, JWST will be located at Earth’s L2 point when it’s finally operational.
If it’s that far away from Earth though, we have to make sure it works perfectly before we launch.
Because we can’t fix it once it’s out there.
Anyway, thanks for watching!