Homework
| Date set/due |
Exercise |
Comments |
| 13th Jan./20th Jan. |
Exercises 7.1,7.2,7.7,7.8 |
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| 20th Jan./27th Jan. |
Exercises 7.20,7.24,7.25,7.26 |
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| 27th Jan./3rd Feb. |
Exercises 7.27,7.29,7.53, 7.55 |
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| 3rd Feb./10th Feb. |
Exercises 7.58, 8.1 and 8.8 |
In 7.58, 8.1, Treat the object as a parallel plate system, neglecting edge effects....
Beware of problem 8.8! Start on it early!
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| 10th Feb./17th Feb. |
Exercises 8.4, 8.6, 8.12 |
Remember to ask me for a hint on a useful coordinate system for 8.12, if you want a hint! And have a think about footnote 12 when you're done. |
| 24th Feb./3rd March |
Exercises 9.12, 9.14, 9.16 |
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| 3rd March/10th March |
Exercises 9.18, 9.19, 9.20, 9.22 |
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| 10th March/31st March |
Exercises 10.3, 10.5, 10.9, 10.14, 10:13, 10:23 and 10:25 |
Lots of extra time to do all this! |
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No homework this week.....midterm study! |
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| 7th April/14th April |
Exercises 11.2, 11.3, 11.4, 11.6, 11.9, 11.13 |
11.2 : The idea here is to think of purely vectorial ways of expressing the results, therefore eliminating all reference to components in some particular coordinate system. 11.4 will need this result. 11.9: First derive a formula for the dipole moment at time t=0 (pi b^2 lambda in the y direction) and then set the thing rotating and write the time dependent expression. Then insert into the general formula 11.60 we've derived (by Friday, I expect). |
| 14th April/28th April |
Exercises 11.14, 12.8, 12.9, 12.20, 12.32, 12.38 (see hint...don't hand that one in),12.46, 12.47, 12.69 (results from 12.38 will help here....) |
Hints:
11.14: First use the parameters of the atom to figure out that the ratio v/c is rather small, and so you can use Larmour. Use the Coulomb force, right? Then write the total energy in terms of the rarius of the orbit, and then equate its time derivative to the power...you should get a differential equation you can solve.
12:38: I'm going to post a scan of 12.38's solution on the totale site. It should be there now.
12:47 Starting point? Set delta=0 in 9.48 and use 12.108 to transform the fields. In the end you should get that the form of the fields is the same in the new frame, but the wave number, amplitude and frequency have been scaled by a velocity dependent factor....but not the speed.... Work out that factor. Now you can answer the rest of the question.
12:69: The zeroth component of the proper force discussed in equations (12.70) and (12.71) is the relativistic power...... Also look at the material from problem 12:38 about the acceleration. I'll tell you that the formula you want to try to propose as the generalization of the Larmour fomula is
K^\mu=(const)\times (alpha^\nu\alpha_\nu)U^\mu
where U is the four-velocity and the constant is the constant stuff in the Larmour formula. Look at the zeroth component of this...it will reduce to Larmour in the small v/c limit, right? Massage the result from 12.38 for the alpha squared quantity and see if you can connect it to the expression in the Lienard formula.
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