Question

A radio receiver antenna that is $2m$ long is oriented along the direction of the electromagnetic wave and receives a signal of intensity $5\times 10^{-16}W/m^2$. The maximum instantaneous potential difference across the two ends of the antenna is

• A. $1.23\mu V$
• B. $1.23mV$
• C. $1.23V$
• D. $12.3mV$

Answer 1

Answer: (A)

$I=\frac{1}{2}{\epsilon }_{0}c{E}_0^2$
$\Rightarrow E_0=\sqrt{\frac{2I}{{\epsilon }_{0}c}}$
$=\sqrt{\frac{2\times 5\times 10^{-16}}{8.85\times 10^{-12}\times 3\times 10^8}}$
$=0.61\times 10^{-6}\frac{V}{m}$
Also $E_0=\frac{V_0}{d}\Rightarrow V_0$
$=E_{0}d=0.61\times 10^{-6}\times 2=1.23\mu V$