Q 12-08-229JEE MainJEE Main 2017 (9 Apr)Easy
A signal is to be transmitted through a wave of wavelength $\lambda$, using a linear antenna. The length $l$ of the antenna and effective power radiated $P_{\text{eff}}$ will be given, respectively, as ($K$ is a constant of proportionality):
Answer: (D) $\lambda,\ P_{\text{eff}} = K\left(\dfrac l\lambda\right)^2$
For efficient radiation the antenna length must be comparable to the wavelength (at least of the order of $\lambda/4$), and the power radiated by a linear antenna varies as
$$P_{\text{eff}} \propto \left(\frac l\lambda\right)^2$$
Only option (4) has this dependence, with $l$ of the order of $\lambda$.
Solution by Sreeraj P, M.Sc Physics