COMMENTS ON SEVENTH PROBLEM SET - SPRING 2003

	Doing the reading from B&B will help greatly, and you might
	notice that several of the problems are similar to examples
	done in lecture.

	7.1 and 7.2, from B&B, are quite basic, requiring only minimal
          number crunching;  in fact, you could easily get two-figure
          accuracy for 7.2 without a calculator.

	7.3 is B&B 4.4 with annotation and a more realistic value for
          the initial radius.  Part (a) is a specific example of the
          "virial theorem," used widely in classical physics (and it
          really is a factor of 8, not 4, in the denominator).

	  Part (c) suggests using the "classical electron radius";
          keep in mind that for this problem, we are merely
          identifying a combination of physical constants that has
          dimension of length, and giving it a name (and a symbol),
          for our convenience.

	  B&B introduce r_e (but which they call r_0) on Page 493, in
          a different context (but one that does involve radiation
          from accelerated charges.  A physical interpretation of r_e
          is the distance that two electrons would have to be apart so
          that their electrostatic interaction energy is equal to the
          rest mass energy of a single electron.  This is a very small
          distance indeed (roughly the nuclear size), and has no
          bearing on this problem (part (e) involves the radius going
          all the way to 0).

	  Sometimes we'll identify the time that it takes light to
          travel this distance, a very short time ineed.

	  Part (c) is answered by solving a separable differential
          equation, which strictly speaking gives t(r), which is
          inverted for r(t).

	7.4:  Some of us would call this a "helix" instead of a
          "spiral", but of course that has nothing to do with this
          problem.  Think of a Slinky.

	7.5:  Consider part (d) to be a strong hint;  this is, in
          doing part (c), you are essentially rederiving the result
          quoted in part (d).  In part (e), you of course want the
          relative amplitude and the phase difference.