March 30, 1998

PHY 712 - Problem Set # 12

Consider a TM wave propagating within a medium having, real dielectric constant $\epsilon$ and permeability $\mu$, along the z axis within an ideal retangular waveguide with a cross section as shown in Fig. 8.5 and with z- component of electric field given by:

$$E_z(x,y,z,t) = E_0 \sin\left(\frac{m \pi x}{a} \right) \sin\left(\frac{n \pi y}{b} \right) e^{i k z -i \omega t}.$$

Here m and n are integers.

1.

Determine the value of k.

2.

Determine the other 5 components of electric and magnetic fields:

(a)

E_x.

(b)

E_y.

(c)

H_x.

(d)

H_y.

(e)

H_z.