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. $1.23\, mV$
• C. $1.23\, V$
• D. $12.3\, mV$

Answer 1

Answer: (A)

$I=\frac{1}{2} \varepsilon_{0} c E_{0}^{2}$
$\Rightarrow E_{0}=\sqrt{\frac{2 I}{\varepsilon_{0} c}}$
$=\sqrt{\frac{2 \times 5 \times 10^{-16}}{8.85 \times 10^{-12} \times 3 \times 10^{8}}}$
$=0.61 \times 10^{-6} \frac{ V }{ m }$
Also $E_{0}=\frac{V_{0}}{d} \Rightarrow V_{0}$
$=E_{0} d=0.61 \times 10^{-6} \times 2=1.23\, \mu V$