Week 8: Faraday’s Law and Induction 295
Finally (and best of all), it looks like changing magnetic fields are somehow able to create electric
fields! Magnetic induction is wonderfully complicated, with right handstwisting this way and that
trying to simultaneously track the directions of currents, magnetic fields, electric fields produced
by the magnetic fields, new currents created by the electric fields,and forces between all of these
currents and the magnetic fields the sit in? And did I mention Lenz’s Law, that makes all of the
induced responses work backwards?
Furthermore, if we look at Maxwell’s equations (so far) we have now seen the full set – two
Gauss Laws, Ampere’s Law, and Faraday’s Law – and there is no sign yet of Maxwell. Wedonotice
that the equations are getting more symmetric. Magnetic fields actually behavealmostlike electric
fields and vice versa and it looks strangely like one can turn into the other if we merely look at it
differently (changing reference frames, for example). However,they aren’t quite right, somehow –
Ampere’s and Faraday’s Law look like theyoughtto be more consistent, but we can’t quite see how.
In a week, we’re going to look at Maxwell’s Equations again and make a startling discovery- the one due to Maxwell – that makes the set of equationsperfectly symmetricexcept for the
lack of magnetic charges, a problem that experimentalists might resolve tomorrow by finding one.
Maxwell’s addition will throw considerablelight^83 on several puzzles in physics, and in the process
give us plenty of stuff to study and learn for the rest of the semester.
But first, let’s look at a complete different topic. Let’s look atharmonically alternating voltages
applied to electrical circuits containing inductances (L), resistors (R), and capacitors (C) as well
as generators or other voltage sources that produce harmonically oscillating voltages. Along the
way we will see how all of the things we have learned so far form pretty muchthe basis for modern
civilization, given that modern civilization would regress to a form not seen for over a century
overnight if our modern electrical power grid were to fail. You are finally knowledgeable enough
to be able tounderstandthe power grid – how electricity is generated, how it is transmitted long
distances without significant losses, how it is used when it gets therein all kinds of work saving
and life saving devices. You can also understand how electrical circuits can be combined to make
information processing devices– radios, televisions, computers, cell phones, music players, networks
- as well as a vast array of devices useful in medicine, business, industry, or the home.
Electricity helps make our cars and boats and planes and trains work, it cools our food to keep
it fresh and cooks our food to make it safe and savory to eat, it cleans our dishes afterwards, it
entertains us in all of the well-lit time we have to spare in the evenings inour electrically heated
or cooled houses, a time when our ancestors only a hundred and fifty years ago either had to work
or sleep for the lack of cheap light, huddling to keep warm in houses heated (if at all) with costly
wood or coal. Electricity saws the wood thatbuildsour houses, it weaves and sews the cloth we
wear on our backs. Electricity enables us to grow far more food than we could without it, transport
that food for vast distances, and store it safely until it is needed –cities would die almost overnight
without it.
Nothing in human civilization is more important than maintaining and increasing the flow of
inexpensive electrical energy. With it, the poorest of our poor arewealthier than the wealthiest
of the kings, emperors, and nobles of yesteryear. Without it, billions of humans would starve, our
urban civilization would collapse, wars would erupt over access to food and other resources that
electricity makes cheap and plentiful.
Yet – to get up, just a bit, on a political soapbox – our elected leadership and the population that
elects them seem somehow to be blind to all of this.Nothingin human civilization is more important
than ensuring an inexhaustible source of electrical energy to enable that civilization to continue, and
yet we do almostnothingwith our collective resources to construct an electrical grid that does not
rely on scarce and exhaustible fuels, fuels that there are far better uses for thanburningthem.
There is plenty of non-scarce energy available on Earth to run a highlevel of civilization not just(^83) Heh, heh. This is a pun, actually. If you don’t get it now, you will. You will.