THE UNIVERSITY OF BRITISH COLUMBIA

*Physics 401 *
Assignment #
**8:**

** GUIDED WAVES **

Wed. 1 Mar. 2006 - finish by Wed. 8 Mar.

Wed. 1 Mar. 2006 - finish by Wed. 8 Mar.

- (p. 405, Problem
**9.25**) -**Group Velocity:**^{1}Assuming negligible damping ( ), calculate the group velocity ( ) of the waves described by Eqs. (9.166) and (9.169):

Show that*v*_{g}<*c*, even when*v*>*c*. - (p. 411, Problem
**9.27**) -**No TE**Show that the mode TE_{00}:_{00}cannot occur in a rectangular wave guide. [*Hint:*In this case , so Eqs. (9.180) are indeterminate, and you must go back to Eqs. (9.179). Show that*B*_{z}is a constant, and hence - applying Faraday's law in integral form to a cross section - that*B*_{z}= 0, so this would be a TEM mode.] - (p. 411, Problem
**9.28**) -**TE Modes:**^{2}Consider a rectangular wave guide with dimensions 2.28 cm x 1.01 cm. What TE modes will propagate in this waveguide, if the driving frequency is 1.70 x 10^{10}Hz? Suppose you wanted to excite only*one*TE mode; what range of frequencies could you use? What are the corresponding wavelengths (in open space)? - (p. 411, Problem
**9.30**) -**TM Modes:**^{3}Work out the theory of TM modes for a rectangular wave guide. In particular, find the longitudinal electric field, the cutoff frequencies, and the wave and group velocities. Find the ratio of the lowest TM cutoff frequency to the lowest TE cutoff frequency, for a given wave guide. [*Caution:*What is the lowest TM mode?]

2006-02-26