Electrodynamics/Tutorials/5/1/1

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Video Intro

Hi, this is Jonathan Gardner.

We're covering [section reference] of Griffiths Introduction to Electrodynamics.

I'm going to move fast, but you can always rewind.

Thumbs up and share if you appreciate my effort.

As always, questions in a video response or comments.

Let's get started.

Magnets are Weird

(Prop: Two magnets, marked so they can see which side is which, and which direction is which. Play with the magnets,)

• Don't think about magnets as you study magnetism: They're weird.
  • Kind of like charges: They attract. (Show them attracting.)
  • But if you turn one of them around, now they repel! (Show them repelling)
  • They're not really just attracting or repelling --- they're actually trying to spin around in my hands! (show it spinning)
  • If you haven't played with magnets before, you need to find some and play with them. I guarantee you, you will have a lot of fun. And that's what physicists do.
  • Magnets remind me of the Rubik's Cube. I can tell there are simple rules that govern things, but I just can't seem to grasp it in my head. Ah well, if you're able to see it, then you must be very smart.

Magnetic Fields

(Put magnets to the side)

• We're not going to start with magnets. It's not the best place to start.
• We're going to start with magnetic fields.
• Magnetic fields are much like Electric Fields, only different.
• If you think about how Coulomb's law works, you have a charge over here and a charge over here and they push or pull on each other.
• But when you think about Electric Fields, then you have a source charge that generates an electric field that the test charge interact with.
• It's a much simpler way to see things. You have fields, which depend on the source charges, and the test charge that interacts with the fields.
• We're going to start with the Magnetic Field, and not even think about how two charges interact without it.
• Unlike electric field, it's really easy to see magnetic fields, using any compass.
  • The compass aligns with the field. North is "forward".
  • The stronger the field, the tighter the compass needle wobbles.
• As for electric fields, the magnetic field weakens rather rapidly, the further you go away.
• If you look at how the field is for these magnets, it almost looks like a dipole. (Draw the field using the compass.)

Currents Generate Magnetic Fields

• Weird thing number one about magnetic fields is that there is no magnetic charge. (Well, aside from monopoles. Ignore that for now.)
• Current going through a wire generates a field. (Setup the current bearing wire.)
• Notice how the compass points.
• This is weird. You can use your right hand to predict the direction of the field. (Show right hand.
• We'll find out the exact rule behind how currents generate magnetic fields later on. For now, just think about how the current, the position vector, and the magnetic field interact with each other. If you're not seeing the cross product, you need to go review it right now.

Magnetic Fields Interact With Currents

• Magnetic fields do not interact with static charges --- charges that are not moving.
• Magnetic fields DO interact with moving charges, currents.
• The force is actually the cross product of the current with the magnetic field.

Two Parallel Wires

Analytically, you can have two wires.

If the current flows in the same direction, then the magnetic field generated by one is like this. And the force is like this. They attract.

If the current flows in the opposite direction, then the force is opposite -- they repel.

Wrapping up

In section 5.1, we're going to look at how currents interact with already existing magnetic fields.

In section 5.2, we're going to see how currents create magnetic fields themselves.

Section 5.3 and 5.4 introduce the magical, magnificient, magnetic potential vector A.

And then in chapter 6 we're going to go back to these magnets I have here. (Play with them some more.)

• Think of the magnetic field as the mitigating thing. Don't think of a particle over here moving causing a particle over there to move. It's not intuitive.

• Velocity of the charge is important, both in producing the field and in interacting with it.
  • wires moving together attract, opposite repel. Wires try to make a circle? What happens when you loop a wire like this... Hum...
• Stationary charges (electrostatics) neither produce a field nor interact with one, which is why we did electrostatics first. Magnetostatics, on the other hand, has no stationary charges, no electric fields, no coulomb forces.

• Later on, we'll see how the Special Theory of Relativity being true creates magnetism, IE, this is really electrostatic forces caused by the speed of light being so slow. (If it were much faster, the magnetic fields would be much, much weaker.)

• Joke at the expense of Astrophysicists.

• Once you've really comprehended magnetism, you get to call yourself a physicist. No other field that I know of really understands magnetism like we do. (Same is true for rotational mechanics, QM and TD, of course.)

Hand-waving about how the forces works.

Understanding how it works relies, entirely, on understanding the interpretation of the cross-product. Notice that if you use your left-hand consistently, it still works... odd... do cross products include information about which hand was used in addition to the magnitude and direction? HUMMMMM....

Overview of the chapter. Mention A vector.

PARALLEL WITH ELECTROSTATICS.

Conclusion

Thanks for watching!

See you in (next section)

Don't forget to try and solve the problems on your own before looking for help.

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See you later. / That's it! / Next time.