Set 1 Due Friday December 5, 2003

• Make a plot in Maple of Good's example 12-3. Use the first 20 non-vanishing terms (1 through 19).[ You can, if need be, find a version of this calculation under the Physics Resource Packets section of my main page (if you need more clues how to do the plot).] If you are masochistic, you can do it in Excel (I tried it but it was too much of a  pain.)
• Write out the series for a cubical box which is grounded on five sides (V=0) and has the 6th side at V=100v. Let the sides of the box be 1.0 m, and let the side be z=1 m where the potential is 100 v. What function must be used in the x-direction?  In the y-direction? In the z-direction in order to satisfy the boundary conditions?
• Show by direct calculation (Griffiths p. 140) that P1(cos theta) is orthogonal to P5(cos theta)
•     a) Suppose the potential on the surface of a sphere is C cos^3 theta. Then follow Griffiths p. 140 to write out the equivalent of (3.72).
•     b) Is 3.72 valid inside the sphere, or outside the sphere, or both?

• Numerically integrate from r=0 to r=0.005 m for a copper wire at  6 kHz, then again at 60 MHz. Graph the magnitude of E vs radius for these two cases.  In the second case, you might want to plot the ln of the magnitude of E vs r.
• Good 16-1
• Good 16.13
• Good 16.10
• Good 16.17

 

• Good 17.1
• Good 17.2
• Good 17.4
• Good 17.12
• Derive Griffiths' 9.180 i  (for Ex) from his 9.179

• Report your results and techniques from the michelson interferometer for microwaves
• RG-35 coaxial cable has an impedance of 21.5 pf/ft and an impedance of 70 ohms. Find R2/R1  and epsilon_r
• Show that T(normal incidence) = 0.96 for n1 = 1 and n2=1.5
• Calculate E(z=1.5 lambda)/E(z=0) for theta_1=60 degrees, n1= 1.4, n2= 1

• Good, 15-1
• Good, 15-2
• Good, 15-3
• Good, 15-5

1. Consider a center-driven antenna, which has a length d equal to ¾ of a wavelength of the driving oscillations. a) Calculate the radiation resistance of this antenna [needs an integral in maple.] b)Sketch the current density distribution in the antenna, and c) plot the angular distribution of the radiated power

2. The directivity of an antenna is defined as the ratio of the maximum value of the power radiated per unit solid angle to the value of the total average power radiated per unit solid angle. Show that the directivity of a simple oscillating dipole is 1.5, whereas the directivity of a half-wave antenna is 1.64

3. Consider two charges, +q and -q separated by a fixed distance d, which rotate at a uniform rate about a common center at an angular rate omega  radians/sec. By thinking of this as two dipoles lying in the same plane, but 90o out of phase, determine the total radiated power, and the angular distribution of power.

4. Calculate and plot the angular distribution of radiation from two half-wave antennas driven in phase and laterally separated by lambda/4.
 

1.  Plot the electric field magnitude for the relativistic motion of a charge moving with constant velocity. This should be a 'polar plot', magnitude vs theta for beta = 0.5, 0.95, and 0.99.

2. Verify gauss's law for the electric field of a moving charge q by integrating over a sphere of radius r surrounding the charge.

3. Work out the transformation of the perpendicular component of the electric field, showing how the field observed in a moving frame is represented in terms of the original E and B fields, and the velocity of the moving frame.