## Lecture 9: Traveling Waves, Maxwell's Equations and Radiation

February 15, 2018

• Read: 14.1--14.2 up to "The Wave Equation"(p.246), 29.1--29.4 (up to the middle of p. 548), 29.5--29.7
• Study: Eqs. 14.1-14.3; Figs. 29.7, 29.10
• Skim: Sections 29.1 and 29.2 and the rest of 29.4

### Objectives

• (Continuing objective) Describe applications of the concepts of induction, waves, and light to everyday real life'' situations.
• Relate the directions and magnitudes of the electric and magnetic fields and of the propagation velocity in a harmonic plane electromagnetic wave. Explain polarization of light and how this relates to the direction of the electric field.
• Explain qualitatively how electromagnetic waves are generated by oscillating charge. From the direction and polarization of an incoming wave, determine possible directions and polarization of a re-radiated wave.
• Explain the differences between the different kinds (radio, light, etc.) of EM waves.
• Correctly convert complex numbers from polar ($Ae^{i\theta}$) form to cartesian (a+ib) form, and vice-versa.
• Given a specific expression for a traveling transverse or longitudinal harmonic wave in sinusoidal or complex exponential form, determine amplitude, angular frequency, frequency, wavenumber, wavelength, period, phase shift and wavespeed.

### Homework

• Friday's Assigned Problems: A27, A31, A39, A48abc, A91, A97abefgh, X1 (CLICK HERE for X1; CH 14: 17, 21; CH 29: 15, 25

Answers: A31 (a) $\pm z$, (b) $\pm x$, (c) $\pm z$, (d) $\pm z$, (e) $\pm x$, $\pm y$; A48 (a) $\lambda = 1257$ nm, $T = 4.19 \times 10^{-15}$ s, $v = 3.0 \times 10^8$ m/s, infrared, (b) $B = 0.2$ mT.

CH 14, number 17: (a) 300 m; (b) 1.58 m; (c) 3.0 cm; (d) 8 microns; (e) 500 nm; (f) 3.0 Angstroms; CH 14, number 21: (a) 1.3 cm; (b) 9.1 cm; (c) 0.20 s; (d) 45 cm/s; (e) -x direction.

Note: If you didn't use the link for problem X1 above, here is another link that you can click on to get you to problem X1.

• Monday's Hand-In Problems: A28, X2 (CLICK HERE for X2); CH 14: 18, 46; CH 27: 18, 34, 38, 44; CH 29: 22

And here is another link that you can click on to get you to problem X2.

### Videos of example problems

To see the problem statement, click on the link below. To play the video example, click on the underlined words "Video Demonstration" near the top of the page with the problem statement.
• Click here for an example of the relation for the electric field in an electromagnetic wave.