Back of the Envelope Estimation Problem for Faraday’s Law

I told my students I would solve this problem for them. It’s a real life problem too.

Is it possible to use a Neodymium magnet and a coil of wire to get an LED to light up?

That’s the real version. But because I was afraid students would be overwhelmed, I added the following:

  • The magnet has a maximum magnetic field of 0.2 Tesla.
  • The LED requires 1.5 Volts and 10 mA to light.

I like this problem because I don’t know the answer. Also, the answer is useful. If you want to do a physics demo showing the voltage induced by a changing magnetic field—what better way than with a hand-held magnet and a small light?

But will it even work? Let’s get started. Here is a diagram.

By changing the magnetic flux through the coil, this will create a curly electric field and an electromotive force (a change in electric potential). The magnetic flux is defined as:

\Phi = N|\vec{B}|A\cos\theta

Where N is the number of turns in the loop, A is the area of the loop and \theta is the angle between the magnetic field and a vector perpendicular to the area. In the diagram above, \theta = 0 since the magnetic field is perpendicular to the coil.

A change in flux produces a voltage according to Faraday’s Law:

\Delta V = \frac{\Delta \Phi}{\Delta t}

Note: yes, I’m different. I think that the number of loops (N) is part of the magnetic flux and that the minus sign in Faraday’s Law doesn’t really mean anything.

Putting the flux into Faraday’s Law, I get (assuming \theta = 0):

\Delta V = \frac{NBA}{\Delta t}

Now for some estimates. I could just estimate everything and then calculate the voltage—but instead I’m going to estimate everything except the number of turns. I can then solve for N and see if it’s reasonable.

Here’s what I have.

  • B = 0.2 T
  • A: radius = 0.01 m
  • Time interval = 1 second
  • Voltage = 1.5 V

Solving for N:

N = \frac{\Delta V \Delta t}{BA}

This is the perfect case to use python for your calculator. You can put your estimates as variables so that you can easily change things up. Here is my code. I get the following output.

Umm….yeah. That’s 23 thousand turns. I’m not going to do that. Even if decreased the time to 0.1 seconds, I would still need 2000 turns. Arg.

Oh, what if I just make a HUGE loop? Nope. That wouldn’t work. In my estimation for the change in flux, I assumed a constant magnetic field—this is obviously not true, but good enough for a small loop. With a big loop, you would have some of the magnetic field creating a negative flux. It would just make things worse.

What if I put the magnet on a spinning stick (run by a motor)?

All About Rhett: A Resume

Who is Rhett? Where is he from? What are his super powers? Why do you want to contact Rhett for your project? Let’s answer these questions.

Super Brief History

How about just the highlights? Yes.

  • Born in the past, not the future.
  • B.S. in physics from Benedictine University (although it was called I.B.C. back then).
  • M.S. in physics from the University of Alabama (including work at CERN).
  • Ph.D. in physics from NC State University.
  • Some other stuff here.
  • Associate Professor of Physics at Southeastern Louisiana University.

Stuff I Do: Blogging

Yes, I like to write. Blogging is the best (for me). It’s quick and free form. You can use a variety of tools (video, gif, graph, python). It’s just the best. THE BEST!

I should probably include some of my favorite posts—but there are just too many that I love. If you want a post on a particular topic (like video analysis)—just google “rhett allain video analysis” and that should get you what you need.

Here is my WIRED blog stuff.

Oh, I also blog here—but I guess you already know that.

Stuff I Do: MacGyver

I am currently the technical consultant for the CBS show MacGyver. It’s a super fun and awesome job. But what do I do? Essentially, I help out with the “MacHacks” in the show. I look over the hacks and see if they are at least plausibly based on some real thing. Other times, I make suggestions for hacks. Finally, I offer suggestions for some of the science-type stuff that MacGyver says.

Oh, I also make DIY home-versions of hacks. Here is an example.

As a bonus, here is an interview I did with CBS KPIX out of San Fransisco on my work with MacGyver.

Stuff I Do: MythBusters

I’ve actually been working on MythBusters much longer than I have worked for MacGyver. I worked on about the last 4 seasons of the original MythBusters and then I did the reboot with Jon Lung and Brian Louden. Finally, I worked on MythBusters Jr.

So, what do I do? Really, there are two things. First thing is to do some background check on future myths. For some myths, I do some estimations and calculations to see if there is a chance of a myth working. You don’t want something that is either too easy or too hard, it should be just right.

The second thing I do is the science explanations. When there is a short explanation about how something works, I help with that.

Stuff I Do: Books

Writing books isn’t as much fun as blogging, but there it is. Here are the books I have authored.

I could talk about books more—but I’m just going to leave it at that.

Stuff I Do: Python and Numerical Calculations

It’s not my fault. If you want to blame someone—how about Bruce Sherwood and Ruth Chabay. It is through their textbook, Matter and Interactions (Wiley), that I was introduced to python and numerical calculations. It’s awesome.

Once you start solving problems by coding, it sort of gets addictive. I’ve been creating python programs since about 2003 (just a guess). Later I started putting more and more of it in my classes—and here we are.

I’m not an expert coder, but I am an expert at implementing this stuff in introductory courses. That’s what I do. I have even held workshops for teachers and educators. It’s fun.

If you want to look at the stuff I’ve done, here are three versions (all online).

  • Physics Python for Mere Mortals. This is an online type book with embedded code. Designed for intro students with zero previous programming experience and some physics. This is what I use in my lecture and lab courses.
  • Introductory Physics with Python. This is more like a full book. It’s incomplete, but the idea is to teach physics using python. I want to work on this some more.
  • Numerical Calculations in Physics. I wrote these as tutorials for students in the calculus based physics course. It uses more vectors and stuff than the over stuff.

Again, I could list a BUNCH more stuff on python but I won’t.

Stuff I Do: Talks

I’ve done quite a few talks. Instead of listing all my talks (or my favorite talks), I’m going to list my favorite topics:

  • The physics of superheroes.
  • The physics of Star Wars and science fiction.
  • Video Analysis (real vs. fake videos).
  • The best physics models (python and stuff) and estimations.
  • Science communication (blogging, MythBusters, MacGyver).
  • The physics of video games.
  • Learning about physics learning (education stuff).
  • Physics demos.
  • Physics and python.

Other Videos

I’m not a huge video guy, but I do make videos. Here is one that turned out better than I expected. It’s a video made at WIRED.

Here is another one that I made (from my youtube channel).

Here is one more. I like to make videos that show physics solutions.

Wait. One more. This one is a more advanced video.

The End.

Contact me if you want to work on something. I’m always looking for extra jobs.

Thanksgiving Physics

I am honestly not quite sure how many blog posts I have about Thanksgiving.  It’s probably about 1 per year for 8 years.  I’m going to guess it’s 8.  Here goes my internet search.

This is what I found.

Video Analysis of Soyuz MS-10

There should be a grave yard for blog posts that start, but never get published.  Fortunately, I have this site.  Here I can share with you my failed posts.  Get ready.

It starts with this epic video from the Soyuz MS-10 failed launch.

That’s pretty awesome.  It’s doubly awesome that the astronauts survived.

Ok, so what is the blog post?  The idea is to use video analysis to track the angular size of stuff on the ground and from that get the vertical position of the rocket as a function of time.  It’s not completely trivial, but it’s fun.  Also, it’s a big news event, so I could get a little traffic boost from that.

How do you get the position data?  Here are the steps (along with some problems).

The key idea is the relationship between angular size, actual size and distance.  If the angular size is measured in radians (as it should be), the following is true L = r\theta where L is the length (actual length), theta is the angular size, and r is the distance.

Problem number 1 – find the actual distance of stuff on the ground.  This is sort of fun.  You can get snoop around with Google maps until you find stuff.  I started by googling the launch site.  The first place I found wasn’t it.  Then after some more searching, I found Gagarin’s Start.  That’s the place.  Oh, Google maps lets you measure the size of stuff.  Super useful.

Finding the angular size is a little bit more difficult.  I can use video analysis to mark the location of stuff (I use Tracker Video Analysis because it’s both free and awesome).  However, to get the angular distance between two points I need to know the angular field of view—the angular size of the whole camera view.  This usually depends on the camera, which  I don’t know.

How do you find the angular field of view for the camera?  One option is to start with a known distance and a known object. Suppose I start off with the base of the Soyuz rocket.  If I know the size of the bottom thruster and the distance to the thruster, I can calculate the correct angular size and use that value to scale the video.  But I don’t the exact location of the camera.  I could only guess.

As Yoda says, “there is another”.  OK, he was talking about another person that could become a Jedi (Leia)—but it’s the same idea here.  The other way to get position time data from some other source and then match that up to the position-time data from the angular size.  Oh, I’m in luck.  Here is another video.

This video shows the same launch from the side.  I can use normal video analysis in this case to get the position as a function of time.  I just need to scale the video in terms of size.  Assuming this site is legit, I have the dimensions of a Soyuz rocket.  Boom, that’s it (oh, I need to correct for the motion of the camera—but that’s not too difficult).  Here is the plot of vertical position as a function of time.sideviewsoyuzaccel.png

Yes, that does indeed look like a parabola—which indicates that it has a constant acceleration (at least for this first part of the flight).  The term in front of t2 is 1.73 m/s2 which is half of the acceleration.  This puts the launch acceleration at around 2.46 m/s2.  Oh, that’s not good.  Not nearly good enough.  I’m pretty sure a rocket has an acceleration of at least around 3 g’s—this isn’t even 1 g.  I’m not sure what went wrong.

OK, one problem won’t stop me.  Let’s just go to the other video and see what we can get.  Here is what the data looks like for a position of one object on the ground.

Data Tool 2018-11-04 13-31-41.png

You might not see the problem (but it sticks out when you are doing an analysis).  Notice the position stays at the same value for multiple time steps?  This is because the video was edited and exported to some non-native frame rate.  What happens is that you get repeating frames.  You can see this if you step through the video frame by frame.

It was at this point that I said “oh, forget it”.  Maybe it would turn out ok, but it was going to be a lot of work.  Not only would I still have to figure out the angular field of view for the camera, but I need to export the data for two points on the ground to a spreadsheet so that I can find the absolute distance between them (essentially using the magnitude of the vector from point A to point B). Oh, but that’s not all.  When the rocket gets high enough, the object I was using is too small to see.  I need to switch to a larger object.

Finally, as the rocket turns to enter low Earth orbit, it no longer points straight up.  The stuff in the camera is much farther away than the altitude of the rocket.

OK, that’s no excuse.  I should have kept calm and carried on.  But I bailed.  The Soyuz booster failure was quite some time ago and this video analysis wouldn’t really add much to the story.  It’s still a cool analysis—I’ve started it here so you can finish it for homework.

Also, you can see what happens when I kill a post (honestly, this doesn’t happen very often).

Actually, there is one other reason to not continue with this analysis.  I have another blog post that I’m working that deals with angular size (ok, I haven’t started it—but I promise I will).  That post will be much better and I didn’t want two angular size posts close together.

The end.

Estimation Posts

Just about everything I write has an estimation – however, I will just list ones that have significant estimations.