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(B) The speed of light in a dielectric medium is given by $v = \frac{c}{\sqrt{\mu_{r} \varepsilon_{r}}}$.Given $\mu_{r} = 1$ and $\varepsilon_{r} = 6.

Vedclass · Accepted Answer

$6$

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(B) The speed of light in a dielectric medium is given by $v = \frac{c}{\sqrt{\mu_{r} \varepsilon_{r}}}$.Given $\mu_{r} = 1$ and $\varepsilon_{r} = 6.25$,the speed $v = \frac{3 	imes 10^{8}}{\sqrt{6.25}} = \frac{3 	imes 10^{8}}{2.5} = 1.2 	imes 10^{8} \, m/s$.For an antenna to radiate effectively,its length $L$ should be at least $\frac{\lambda}{4}$.Thus,$\lambda = 4L = 4 	imes 5.0 	imes 10^{-3} \, m = 20 	imes 10^{-3} \, m = 0.02 \, m$.The frequency $f$ is given by $f = \frac{v}{\lambda} = \frac{1.2 	imes 10^{8}}{0.02} = 60 	imes 10^{8} \, Hz = 6 \, GHz$.

An antenna is placed in a dielectric medium of dielectric constant $6.25$. If the maximum size of the antenna is $5.0 \, mm$,what is the minimum frequency of the signal it can radiate in $GHz$? (Given $\mu_{r} = 1$ for the dielectric medium)

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