Where $$k = \,\,\eta \,\omega \,\, \in $$

(a) Determine the surface charge densities $${\rho _s}$$ on the plates at x = 0 and x = d

(b) Determine the surface current densities $$\mathop {{J_s}}\limits^ \to $$ on the same plates.

(c) Prove that $${\rho _s}$$ and $$\mathop {{J_s}}\limits^ \to $$ satisfy the current continuity condition.

Where $$k = \,\,\eta \,\omega \,\, \in $$

(a) Determine the surface charge densities $${\rho _s}$$ on the plates at x = 0 and x = d

(b) Determine the surface current densities $$\mathop {{J_s}}\limits^ \to $$ on the same plates.

(c) Prove that $${\rho _s}$$ and $$\mathop {{J_s}}\limits^ \to $$ satisfy the current continuity condition.

Where $$k = \,\,\eta \,\omega \,\, \in $$

(a) Determine the surface charge densities $${\rho _s}$$ on the plates at x = 0 and x = d

(b) Determine the surface current densities $$\mathop {{J_s}}\limits^ \to $$ on the same plates.

(c) Prove that $${\rho _s}$$ and $$\mathop {{J_s}}\limits^ \to $$ satisfy the current continuity condition.

(a) Calculate the cut-off wavelength and the guide wavelength for this mode.

(b) What are the other (TE or TM) modes that can propagate through the waveguide?

(c) If a = b = 2.29 cm, what are the modes which can propagate through the waveguide?