COMMENTS ON PROBLEM SET 8 - FALL 2002 8.1 (B&B 5.1): In the figure, note the little arrow tangent to the ellipse in the third quadrant at the left. This should indicate the phase difference between E_(inc,x) and E_(inc,y). Part (c) asks for a pressure, and there are many ways to express the result. The example on Pages 324-327 exhibits pressure as a vector parallel to the vector S, and some of us don't like this one bit. Pressure is, strictly speaking, a tensor, and the direction of the force on the plate is a contraction of this tensor with the direction normal to the surface. If this sounds too hifalutin', consider the direction of the force if the incidence were not normal (demonstrated in lecture with resort to carcinogens). 8.2 (B&B 5.2): The phrasing of the problem may be subject to interpretation. The usage "Indicate the magnitude and direction of the Poyting's vector ..." should be taken to mean "For the times indicated, make a sketch of the Poynting Vector's magnitude and direction along the length of the cable." That is, you should be able to find, within a mulitplicative constant, S_z(z,t) (I'm inventing "z" as the independent variable representing extent along the line - do what you prefer) and make sketches of this field, indicating relative amplitude and direction, as a function of z for the given times. Since you're doing this over an entire period, any extra phase shouldn't matter, but you could make things easier on yourself and the grader if you pick and identify a convenient phase. This matters more, but not much more, in the second part of the problem. 8.3 (B&B 5.3): This calculation is a bit trickier than those done in the text (coax cable, infinite parallel plates). You'll need to recall some basic properties of electric and magnetic fields due to long straight wires (from 8.02, 8.022 or the equivalent). Consider that your answers will involve logarithms if you need a reminder of the functional nature of the E&M fields between the wires in the plane containing the wires. In doing the needed integrals to find C_0 and L_0, be sure to set up the integrals carefully, and watch the signs (if you get either quantity equal to zero, or negative, look for the signs). Personally, I found the L_0 integral easier, but the mechanics of integration are the same for both. As a check in the numerical answer, would you expect an answer greater or less than the free-space impedance of 377 Ohm? 8.4 (B&B 5.4): This is essentially a derivation of a result cited in the text, and I won't tell you where. If you don't read the text, think ahead and see what relation part (c) has to the provided expressions for E_y.