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 mV
• B. 1.23 mV
• C. 1.23 V
• D. 12.3 mV

Answer 1

The correct option is A

1.23 mV

$I=\frac{1}{2}{ϵ}_{0}C{E}_0^2$

$\Rightarrow E_0=\sqrt{\frac{2I}{{ϵ}_{0}C}}=\sqrt{\frac{2\times 5\times {10}^{-16}}{8.85}}=0.61\times {10}^{-6}\frac{V}{m}$

Alsop $E_0=\frac{V_0}{d}\Rightarrow V_0=E_{0}d=0.61\times {10}^{-6}\times 2=1.23\mu V$