PHY425 Homework

# PHY425 Homework

Late homework will not be accepted!
1. Inductance due on Tue Jan. 29, 08.
Problems: 7.22, 7.23, 7.21, 7.24a (symbolic solution sufficient), 7.25a, 7.20a.
2. Energy of Magnetic Field due on Tue Feb.5, 08.
Problems: 7.26abc, 7.27, 7.28 [tip: volume current; use Ampere's Law to calculate B(s); calculate W; determine L], 7.29.
3. Maxwell's Equations due on Tue Feb.5, 08.
Problems: 7.31, 7.34 [tip: radial component of E = - ( theta(v t - r) - theta(-r) ) q / (4 pi epsilon_0 r^2 ); d(theta(x))/dx = delta(x) ].
4. Conservation Laws due on Tue Feb.19, 08.
Problems: 8.2 [anwsers to (a) needed for (b) and (c): E = I t / (epsilon_0 pi a^2); B = mu_0 I s / (2 pi a^2) where s is the distance from the wire axis],
8.3 [hints: inside the sphere B = 2/3 mu_0 sigma R omega z-hat; outside: B = mu_0 * m / (4 pi r^3) * ( 2 cos(theta) r-hat + sin(theta) theta-hat ) where m=(4/3 pi R^3)(sigma omega R)],
8.8a [hint: outside the sphere B is given in the hints to 8.3 with m=(4/3 pi R^3) M ]
5. Electromagnetic Waves I due on Tue Mar 4, 08.
Problems: 9.2, 9.9, 9.12.
6. Electromagnetic Waves II due on Tue Mar 25, 08.
Problems:
9.16 (check your derivations, the right formula for R: R=[(1-alpha*beta)/(1+alpha*beta)]^2),
9.19 (see Tables 4.2, 6.1, 7.1 for propetries of water; in point (c) compare B_0/E_0 ratio in metal and vacuum).
7. Potentials I due on Tue Apr 1, 08.
Problems:
10.3, 10.5, 10.10 (Answer E = - mu_0 * k * ln(b/a) / (2 * pi) in -x direction).
8. Potentials II due on Tue Apr 8, 08.
Problems: 10.13, 10.14, 10.18.
9. Radiation due on Tue Apr 29, 08.
Problems:
11.9 (Hint: Start by calculating a vector of electric dipole moment for stationary ring. Then take into account its rotation. Finally calculate appropriate time derivatives.)
11.15 Skip the last question about ratio of intensities. (Hint: Obtain formula for cos(theta_max) for arbitrary beta (first task). For the 2nd task, set beta = 1 - epsilon, where epsilon << 1, and expand in powers of epsilon neglecting higher order terms. Use also cos(theta) = 1 - theta^2/2 approximation (valid for small theta). At the end substitute epsilon = 1 - beta.)