Q 12-08-122JEE MainJEE Main 2022 (24 Jun, Shift 2)Medium
An antenna is placed in a dielectric medium of dielectric constant $6.25$. If the maximum size of that antenna is $5.0\ \text{mm}$, it can radiate a signal of minimum frequency of ______ GHz. (Given $\mu_r = 1$ for dielectric medium)
Numerical value type. Enter your answer.
Answer: 6
Speed in the medium: $v = \dfrac{c}{\sqrt{6.25}} = 1.2\times10^8\ \text{m s}^{-1}$.
Antenna length $= \dfrac\lambda4$, so the largest wavelength is $\lambda = 4\times5\ \text{mm} = 0.02\ \text{m}$.
$$f_{\min} = \frac{v}{\lambda} = \frac{1.2\times10^8}{0.02} = 6\times10^9\ \text{Hz} = 6\ \text{GHz}$$
Solution by Sreeraj P, M.Sc Physics