Charges, Loops and a Wave With Nothing to Wave
Last timeThe Ring That Forgets
Two rules about loops say that a changing magnetic field makes an electric one and a changing electric field makes a magnetic one. Together they force a wave with no medium.
Every wave in this course so far has waved something. Beads, a rope, a column of air,
a ring of metal: in each case there was a material, and the rule was a statement about
a point and its neighbours in that material. This lesson arrives at a wave with no
material, and the surprise is that it needs no new machinery to do so. It needs two
statements about loops.
- how much the electric field loops around a small circle. If this is not zero, a charge carried once round that circle comes back having gained energy, which is what drives current in a loop of wire
- how fast the magnetic field through that circle is changing, with a minus sign. The loop of electric field opposes the change rather than assisting it, which is what makes the pair restore instead of run away
- the two constants, one measured with magnets and steady currents and one with charges at rest. Together they are the only numbers in the pair of rules, and they will turn out to set the speed
- how fast the electric field is changing. This is the term that had to be added for consistency and that makes everything in this lesson possible
The loop that closes
The two rules are worth drawing as a cycle, because that is what they are.
The halfway house: a loop and a pair of plates
Before removing the apparatus altogether it is worth watching the cycle in a circuit,
where it is easy to believe. Charge sits on two plates and makes an electric field
between them. Released through a coil, the current builds a magnetic field, which
resists being changed and so keeps the current going past the point where the plates
are empty, charging them the other way.
The lesson stops here
4 more paragraphs to go
You have read the opening. The rest of the argument, the problems that check whether it landed, and the lines worth keeping at the end all come with a plan.
The first lesson of every course in the library reads the whole way through, free, so you can see exactly what the rest of them are.
See the planThe contentsThis is the reading half
Starting the course gives you your own copy of it. Every idea on every page has problems standing under it, marked with a reason rather than a tick, and any sentence you do not believe can be opened and argued with. None of that can happen on a page nobody owns.
The contents