Physics H131: Problem Set #6

Due: Friday, Oct. 17, 2008 in class or by 5pm in the PRB main office.
Check the H131 web page for hints and suggestions.

Full credit: 100 points

The problems on this set are worth 120 points if you include the "challenge" problem (20 pts.). For full credit you must solve enough problems to obtain 100 points. If you earn more than 100 points, the extra points can help you offset points lost elsewhere.

You can (and should!) discuss the problems with other students of your class, but you must write down the solutions in your own words. For synthetic, rich context or advanced problems, provide a complete solution, with a picture and a final check of your results, following the general problem-solving framework discussed in class. Please study the examples on pp. 126-129 and pp. 147-149 for guidance.

Short-Answer Questions

Give a short (not more than two sentences) but accurate explanation for each problem or question!

• Two-minute problem: C9T.8 (p.169) [5 pts.]

Chapter C8 Problems

• Synthetic: C8S.5 (p.151) [15 pts.]
• Synthetic: C8S.7 (p.151) [20 pts.]

Chapter C9 Problems

• Basic: C9B.2 (p.169) [5 pts.]
• Basic: C9B.3 (p.169) [5 pts.]
• Basic: C9B.6 (p.169) [10 pts.]
• Synthetic: C9S.7 (p.171) [20 pts.]
  This is a problem which involves only symbolic manipulation (no insertion of numbers in the final result).
• Synthetic: C9S.10 (p.171) [20 pts.]
  (In this problem you prove Eq.(C9.18). The proof is not difficult if you follow the instructions, but it is a valuable exercise in rearranging sums and working with dot-products.)

Extra Credit

• Advanced: C9A.2 (p.172) [20 pts.]
  If you can, please use calculus (integration) to do this problem. This provides the shortest solution. Otherwise, follow the hints given in the problem. Note a typo in this problem: four lines above Fig. C9.13, the expression for m_j should involve the ratio r_j/R and not the square of this ratio!