Question

A rectangular metal wave guide filled with a dielectric material of relative permittivity ${ϵ}_r=4$ has the inside dimensions 3.0 cm $\times$ 1.2 cm. The cut-off frequency for the dominant mode is

Answer 1

Ans : (a)

$v=\frac{c}{\sqrt{{ϵ}_r}}=\frac{3\times {10}^8}{2}=1.5\times {10}^8$

$f_c=\frac{v}{{\lambda }_c}=\frac{1.5\times {10}^8}{6\times {10}^{-2}}=2.5GHz$

or $f_c=\frac{v}{2a}=\frac{1.5\times {10}^8}{6\times {10}^{-2}}=2.5GHz$