JEE Main · 2022 · 24 Jun 2022 · Shift 1 · EM Waves

In amplitude modulation, the transmitted signal contains the carrier frequency and sidebands at $f_c\pm f_m$. Since $f_m\ll f_c$, the effective transmission frequency is approximately $f_c=3.5$ GHz.

The minimum antenna length is $\frac{\lambda }{4}$ where $\lambda =\frac{c}{f_c}$:

$\text{Minimum length}=\frac{\lambda }{4}=\frac{c}{4f_c}=\frac{3\times 10^8}{4\times 3.5\times 10^9}$

$=\frac{3\times 10^8}{14\times 10^9}=\frac{3}{140}\times 10^{-1}=0.0214$ m $=21.4$ mm

The answer is (C) 21.4 mm.