Question

A radio receiver antenna that is 2 m 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

The correct option is A $1.23\mu V$

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