This preview shows pages 1–4. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Scott Hughes 4 May 2004 Massachusetts Institute of Technology Department of Physics 8.022 Spring 2004 Lecture 21: Polarization & Scattering 21.1 Summary: radiation so far In the last few lectures, we examined solutions of the source free Maxwell equations: ~ ~ E = 0 ~ ~ E = 1 c ~ B t ~ ~ B = 0 ~ ~ B = 1 c ~ E t . With a little massaging, we discovered that these equations can be rewritten as wave equa tions for ~ E and ~ B : 2 ~ E t 2 c 2 2 ~ E = 0 2 ~ B t 2 c 2 2 ~ B = 0 . A particularly instructive solution to the wave equations are the plane wave forms: ~ E ( ~ r, t ) = ~ E sin( ~ k ~ r t ) ~ B ( ~ r, t ) = ~ B sin( ~ k ~ r t ) . This solution represents an electromagnetic wave propagating in the k = ~ k/k direction (where k = q ~ k ~ k = q k 2 x + k 2 y + k 2 z ). By considering how the wave behaves at some fixed time, we learned that k is simply related to the wavelength : k = 2 / . The requirement that this solution satisfy the wave equation lead us to the condition = ck . From the definition = 2 (angular frequency is 2 radians times regular frequency), we then obtain = c . Finally, requiring that the plane wave solution satisfy all of Maxwells equations leads to some important constraints on the vector amplitudes ~ E and ~ B . These constraints are: The amplitudes are orthogonal to the propagation direction: k ~ E = 0, k ~ B = 0. The amplitudes are orthogonal to each otherL ~ E ~ B = 0. The amplitudes have the same magnitude:  ~ E  =  ~ B  . The propagation direction is parallel to ~ E ~ B . These are important and rather constraining conditions. Nonetheless, they leave us with a great deal of freedom in the amplitudes. This freedom is described in terms of the radiations polarization state . 21.2 Linear polarization Since plane waves propagate in a straight line, we might as well just define their propagation direction as something simple and be done with it. In what follows, we will take k = z , so our wave is of the form ~ E = ~ E sin( kz t ) ~ B = ~ B sin( kz t ) . Suppose that the wave is arranged (somehow) so that the electric field is aligned with the x axis: ~ E = E x . Then, our requirement that ~ E ~ B be parallel to k tells us that ~ B = E y . (Were also using  ~ E  =  ~ B  .) This configuration is known as a linearly polarized wave, as the electric (and magnetic) fields at all points align parallel to a line. Such an electromagnetic wave is quite simple to produce: we just need to take a conductor and arrange things so that it has an oscillating charge distribution. Heres an example: + + + + + + t = 0 t = t = /2 The top part of this figure shows an antenna : a long conductor in which we drive a very rapidly oscillating current, so that the conductor has a charge distribution . As we move to the right, time increases.the right, time increases....
View
Full
Document
This note was uploaded on 04/11/2008 for the course PHYSICS 8.022 taught by Professor Hughes during the Spring '08 term at MIT.
 Spring '08
 Hughes
 Mass, Polarization, Radiation

Click to edit the document details