Chapter 23.4, Problem 1cTH

A long, thin steel wire is cut in half, and each half is connected to a different terminal of a light bulb. An electromagnetic (EM) plane wave $\left(\stackrel{\to }{E}\left(x,y,z,t\right)=E_o\sin \left(kx-\text{ω}t\right)\hat{y},\stackrel{\to }{B}\left(x,y,z,t\right)=B_o\sin \left(kx-\text{ω}t\right)\hat{z}\right)$moves past the wire, as shown.

c. Suppose instead that the wire were positioned as described below. Would the brightness of the bulb be greater than, less than, or equal to the brightness that it had in part b? Explain your reasoning in each case.

i. The wire is parallel to the y-axis but with its bottom end located on the x-axis (i.e., the wire is shifted up ward a distance equal to half its length).
ii. The wire is tilted so that it makes an angle of 40° with respect to the y-axis but is still parallel to the y−z plane. (See diagram at right.)