The Virtuosi (Posts about magnetism)https://thephysicsvirtuosi.com/enContents © 2019 <a href="mailto:thephysicsvirtuosi@gmail.com">The Virtuosi</a> Thu, 24 Jan 2019 15:05:01 GMTNikola (getnikola.com)http://blogs.law.harvard.edu/tech/rss- Esoteric Physics I - The Hall Effecthttps://thephysicsvirtuosi.com/posts/old/esoteric-physics-i-the-hall-effect/Jesse<p>What we usually do here at the The Virtuosi is take an interesting
problem, and work out the physical principles behind what we're seeing.
Or pose a question and try to answer it. Now, I'm a big fan of this kind
of thing, which is why I've done so much of it. But I worry that it
might give a slightly skewed view of physics. Sure, physics explains
things. That's why we do it. But not everything in physics is <a href="http://thevirtuosi.blogspot.com/2010/04/laser-gun-recoil-follow-up.html">laser
guns</a>
and <a href="http://thevirtuosi.blogspot.com/2010/05/solar-sails-i.html">solar
sails</a>.
There are a lot of interesting physics phenomena that the general public
will never hear about, because they're just too, well, esoteric. What
I'm going to do is occasionally talk about such effects, and, for some
of them, give you applications for these strange effects you might see
on a day-to-day basis. Today I'm going to examine the Hall effect. The
Hall effect is simple, as these things go, once we understand the
pieces. The first piece is that magnetic fields deflect moving
electrically charged particles. I don't think I can give you a good
simple reason for this, you're just going to have to trust me (for those
interested, I'd argue that the relativistic transformation of a magnetic
field is an electric field, and that will certainly deflect an
electrically charged particle). This is a piece of the Lorentz force.
The next piece that we need to know is that opposite electrically
charged particles attract. So a positively charged particle attracts a
negatively charged particle. Knowing those two things we can detail the
Hall effect.
<a href="http://4.bp.blogspot.com/_SYZpxZOlcb0/S_nxJSw3bQI/AAAAAAAAABU/Mi2_jDtskus/s1600/Hall+effect+pos.JPG"><img alt="image" src="http://4.bp.blogspot.com/_SYZpxZOlcb0/S_nxJSw3bQI/AAAAAAAAABU/Mi2_jDtskus/s320/Hall+effect+pos.JPG"></a>
Take the slab pictured above. We run an electric current through it.
Conventionally we take current as moving positively charged particles.
There is a magnetic field into the screen. This deflects the positive
charges up the screen, as shown, with some upward force. Over some time,
we will accumulate positive charges at the top. Because there is no net
charge in our slab, this must leave a region of negative charge at the
bottom. These regions of charge will attract, and cancel out the force
from the magnetic field. This charge separation results in a voltage
differential between the two sides of the slab, which is what we
actually measure. The Hall effect has some nifty consequences
physically. I mentioned that conventionally we take current to be
positive particles moving. A microscopic picture of our conductors will
tell us that, in general, electrons are what we consider to be flowing
in an electric current. Now, it turns out that our magnetic field will
deflect electrons moving opposite our current direction (negative
current moving backwards is the same as positive current moving
forwards) to the same side as our hypothetical positive particles got
deflected to. This generates a charge differential with negative and
positive charges on the opposite sides of the slab (shown below), which
means the voltage is negative what we would have measured above! This
means we expect to get a certain sign of the measured Hall voltage,
which we can predict. This sign would correspond to negative particles
(electrons) being the moving charge carriers in substances. It turns out
that there are some substances (some semiconductors) where the sign of
the Hall voltage is opposite what we expect from electrons. This means
that in those substances the current is being carried by positive
particles! I won't explain what that means here (I may address that in a
later post), but I hope you can see why that would be fascinating. We
expected to have electrons moving, and it turns out that something else
is really doing the moving. The Hall effect is an experimental result
that helped suggest a whole new way of thinking about conduction in
materials.
<a href="http://2.bp.blogspot.com/_SYZpxZOlcb0/S_nxRTxhhoI/AAAAAAAAABc/AJGpkjd-iWU/s1600/Hall+effect+neg.JPG"><img alt="image" src="http://2.bp.blogspot.com/_SYZpxZOlcb0/S_nxRTxhhoI/AAAAAAAAABc/AJGpkjd-iWU/s320/Hall+effect+neg.JPG"></a>
Beyond being very interesting physics, there are some applications to
this effect. It is an easy way to create a magnetic field sensor. Take a
slab of material, run a current through it, and measure the voltage on
the sides. Where do we use magnetic field sensors? Well, they sometimes
show up as a way to tell if something is open or closed. Put a magnet in
your lid, and a Hall effect sensor in the lip the lid rests on. When it
is closed, you'll measure a voltage, and when it is open you won't. Now
you can tell if it is open or closed. A little imagination, and you can
see how this would be useful for all kinds of switches. Hit the switch,
move your magnet, and change your voltage. According to Wikipedia, Hall
effect switches are used in things as diverse as paintball guns and
go-cart speed controls. They could also be used as a speed or
acceleration measurement in a rotating system. Attach a magnet to the
rotating object, put a sensor at a fixed location, and measure how the
voltage in your sensor changes as the object sweeps past it. There are
many more applications, but this is just to give you a taste of how this
seemingly esoteric physics concept may show up in your everyday life.
It's not just the interesting problems we often work on this blog,
physics is everywhere. In many different guises</p>currentesoterichall effectmagnetismhttps://thephysicsvirtuosi.com/posts/old/esoteric-physics-i-the-hall-effect/Sun, 23 May 2010 23:31:00 GMT
- Another Reason Why The Core is Stupidhttps://thephysicsvirtuosi.com/posts/old/another-reason-why-the-core-is-stupid/Alemi<p><a href="http://4.bp.blogspot.com/_YOjDhtygcuA/S8d8LoMoWHI/AAAAAAAAAJg/3HSwL_rBMFE/s1600/The_Core_poster.jpg"><img alt="image" src="http://4.bp.blogspot.com/_YOjDhtygcuA/S8d8LoMoWHI/AAAAAAAAAJg/3HSwL_rBMFE/s320/The_Core_poster.jpg"></a>
I assume everyone has heard of <a href="http://en.wikipedia.org/wiki/The_core">The
Core</a>, the terrible scifi movie
from 2003. If you haven't you're missing out on what appears to be,
according to Discover magazine, <a href="http://discovermagazine.com/2007/nov/none-found">the worst sci-fi film
ever</a>. There are
already numerous sites that discuss the bad science in the core
(<a href="http://geolor.com/The_Core_Movie-Facts_and_Fiction.htm">here</a>, or over
at <a href="http://www.badastronomy.com/bad/movies/thecore_review.html">Bad
Astronomy</a>),
but they all seem to ignore another fundamental problem with the plot. I
don't think I'll give too much away if I tell you that the basic premise
of the movie is that the earth's core has stopped rotating, and so the
earth's magnetic field is collapsing, which they claim will mean that
all of the previously deflected microwaves (note: EM radiation is not
bent by a magnetic field) will cook us all. Now, a lot of people have
focused on the microwaves bit, which while bad science, one could argue
that we would still have some bad effects from loosing our magnetic
field. The problem I have is that the Earth's magnetic field cannot
change that abruptly. I'm currently teaching undergraduate honors E&M,
and we're working out of the fantastic texbook (unfortunately now out of
print) by
<a href="http://books.google.com/books?ei=tn7HS87OGYKuygS9yqCNCw&cd=1&id=3LYRAQAAIAAJ&dq=Purcell+Electromagnetism&q=#search_anchor">Purcell</a>.
And in the chapter on electromagnetic induction he has an illuminating
exercise. Lets try and estimate how quickly the magnetic field of the
earth can change. Well, lets sort of work backwards. We know that if we
have a conducting ring with a current flowing through it, this will
create a magnetic field. So, if we can try and model some sort of
circuit that approximates the earth, and then look at how quickly energy
is dissipated in that circuit, we can estimate how fast the magnetic
field decays. So lets imagine a thick torus with height and width a.
Flowing around this torus is some current I, distributed in a
complicated way. The torus is made out of a material with some
conductivity sigma. Now, we know that for a wire made out of some
material with a conductivity sigma, we can estimate its resistance as $$
R = \frac{ L }{ \sigma A } $$ where L is the length, and A is the
cross sectional area of the wire. Lets do that with our torus, calling
$$ A = a^2 \qquad L = 2 \pi a $$ giving us a resistance $$ R \sim
\frac{ 2 \pi }{ \sigma a } $$ To estimate the magnetic field of this
torus, lets just take the magnetic field of a loop with radius a/2. I.e.
$$ B = \frac{ \mu_0 I }{2 \pi (a/2) } $$ Now we know that the energy
stored in the magnetic field is $$ U = \frac{1}{2 \mu_0 } \int B^2
\ dV \sim \frac{1}{2 \mu_0} B V $$ where we take the magnetic field
to be the magnetic field of the simple loop and V to be the volume of a
fat cylinder or so, i.e. $$ V \sim \pi a^2 \times a $$ Now if we
have a circuit with a known resistance we know that the energy is
dissipated through the resistor $$ \frac{dU}{dt} = - I^2 R $$ so if we
just want an order of magnitude estimate for the characteristic decay
time, we can take $$ \tau \sim \frac{ U }{ I^2 R } $$ Putting in our
approximations from above we have $$ \tau \sim \frac{
\frac{1}{2\mu_0 } B^2 V }{ I^2 \frac{2 \pi }{ \sigma a } } =
\frac{ \frac{1}{2 \mu_0 } ( \pi a^3 ) \left( \frac{ \mu_0 I }{
2 \pi (a/2) } \right)^2 }{ I^2 \frac{ 2 \pi }{\sigma a} } =
\frac{ \mu_0 }{4 \pi^2 } \sigma a^2 $$ where we know $$ \mu_0 =
4 \pi \times 10^{-7} N/A^2 $$ we obtain roughly (i.e. ignoring the
other pi) $$ \tau \sim \sigma a^2 \times 10^{-7} (s) $$ Now, lets
take the radius of the core to be about half the radius of the earth, or
3000 km or so, and take the conductivity of the core to be about a tenth
of that of iron at room temperature (iron becomes a worse conductor when
its heated), i.e. $$ a \sim 3000 (km) \qquad \sigma \sim 10^6 (S/m)
$$ We obtain $$ \tau \sim 10^12 (s) = 300 (centuries) $$ So, even if
you could magically make the core of the earth stop spinning, the
magnetic field is not going to change instantaneously, in fact it would
only be able to change on the order of 300 centuries or so. This is
really short on geologic time scales, but nothing like the week or so
that the movie The Core takes place over. Just one more reason why one
of the worst sci-fi movies of all time is bad.</p>bad physicsfermi problemfunmagnetismmovieorder of magnitudesci-fithe corehttps://thephysicsvirtuosi.com/posts/old/another-reason-why-the-core-is-stupid/Thu, 15 Apr 2010 17:30:00 GMT