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14 December 2009

First contact with E&M

In AP physics B, it's time to start electricity. The portion of the course dealing with electricity and magnetism is a non-negligible 25% of the exam.  This is also the most difficult section of the course, because it deals with such abstract concepts as "charge" and "field".  I still do as many quantitative demonstrations as I can, especially with magnetic forces and electric circuits.  But when it comes down to it, it's not straightforward to give my students an easy mental picture of, say, a +0.2 μC charge at rest in a 200 N/C electric field.

On the first day that I broach the subject of electricity, therefore, I try to make the explicit connection between electricity, magnetism, and MECHANICS.  I point out that the whole point of the E&M unit is to apply the mechanics we've learned to a new and strange regime, that of charges.  It requires a considerable leap of faith and reasoning to deal with a problem as simple as, "a proton at rest experiences a force of 10-17 N to the right.  What is its speed after 10-15 s?"  Because it's a proton, and because the numbers are "so small," suddenly the concepts of Fnet=ma and kinematics become impossible.

So my very first quantitative demonstration is done with the PASCO e/m device, pictured above.  This is an expensive but worthwhile item.  I put in a capital request a few years ago, and the money came through.  Purchasing one of these would be good use of grant money.  Or, if you can't find the money to buy one of your own, check with the local college's physics department -- most colleges have large numbers of these lying around for use in the freshman lab, and you may be able to borrow one for a week.

Now, this device can do many awesome things.  You can deflect electrons electrically with charged plates; or, you can use a magnetic field to bend electrons in a circle.  The relevant voltages and magnetic fields are either printed right on the device, or are read clearly off of the power supplies.  Certainly this would be a good demonstration in the magnetism section, to show that you can in fact predict the magnetic field given the radius of electrons' circular motion, or to predict the speed of electrons in a circle, or to verify the equation for electrical potential energy, qV.  But at the begninning of the unit, all these concepts are completely foreign.  I do something much, much simpler.

All I tell the class is that I have electrons that have been given a kinetic energy of 4 x 10-17 J.  (Sure, I figured that out using qV... but I say NOTHING about that to the class.)  Then, I tell the class that these electrons experience a magnetic force that acts as a centripetal force, and that is equal to qvB.  I tell them the value of this magnetic field thing labeled as B, which equals 7.8 x 10,-4 T. 

The question:  what is the radius of the electrons' circular motion?

We follow a Newton's Second Law approach, drawing a free body diagram, setting the net force equal to ma, where acceleration is v2/r.  We solve in variables first to get r=mv/qB. We use the definition of kinetic energy (and the looked-up mass of the electron) to calculate the speed of the electrons.  We look up the charge of the electron.  Plugging in, we find that the radius of the circular motion should be in the neighborhood of 6 or 7 cm. 

Then I turn on the device and hit the lights.  We see a dim greenish circle inside the big globe, a circle of diameter that we measure to be... between 12 and 14 cm. 

Follow-up questions that I ask right there:  1. If I increase the magnetic field thingy, what should happen to the circle of electrons?  Well, since B is in the denominator, the radius should get smaller.  (Then I increase the current to the Helmholz coils, increasing the magnetic field, and the circle gets tighter.)  2. If instead I give the electrons more kinetic energy, what should happen to the circle of electrons?  Well, increasing the kinetic energy increases the electrons' speed.  Since v is in the numerator, the circle's radius should get bigger.  (Then I increase the voltage on the electron gun, increasing the electrons' speed, and expanding the circle.)

This demonstration provides a nice "gee, wow" effect, while hammering the point:  once an electricity or magnetism problem can be phrased in terms of forces or energies, then it becomes a mechanics problem -- and we already know how to deal with those.

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