THE UNIVERSITY OF BRITISH COLUMBIA

*Physics 401 *
Assignment #
**9:**

** LOOSE ENDS & COAX CABLES **

Wed. 8 Mar. 2006 - finish by Wed. 15 Mar.

Wed. 8 Mar. 2006 - finish by Wed. 15 Mar.

**Cutoff Frequencies:***Explain in words*why there is a*lower*limit on the frequencies of EM waves that will propagate freely either through a*tenuous plasma*or down a*rectangular waveguide*. Why is there*no*cutoff frequency (neither upper nor lower) for wave propagation down an ideal*coaxial cable*?**Rectangular Waveguide with Dielectric:**Show that if a hollow rectangular waveguide of the type shown in Griffiths' Figure 9.24 is completely filled with a dielectric of permeability , its cut-off frequency is*lower*than if it were empty, by a factor of :

Thus, for a given operating frequency, a dielectric filled waveguide can be*smaller*than an empty one.- (p. 412, Problem
**9.31**) -**Coax Cable:**^{1}- Show directly that Eqs. (9.197) satisfy MAXWELL'S EQUATIONS (9.177) and the boundary conditions (9.175).
- Find the net charge per unit length, ,
and the net current,
*I*(*z*,*t*), on the inner conductor.

**Coax Impedance:***a*is the radius of the inner coax line and*b*is the radius of the outer coax cylinder, as shown.In general, the characteristic impedance of a transmission line is given by

Show that the characteristic impedance of this coax line satisfies this definition by calculating and explicitly, and then

*Z*.

2006-03-05