Question

In a radio wave if E=10^-4 V/m, Then find the magnitude of poynting vector?

Answer 1

Since, in a radio wave $\overrightarrow{E}\bot \overrightarrow{B}$ and Poynting vector is defined by

$$\overrightarrow{S}=\frac{1}{\mu_0}(\overrightarrow{E}\times\overrightarrow{B})\\ \implies ||\overrightarrow{S}||=\frac{1}{\mu_0}||\overrightarrow{E}||\cdot||\overrightarrow{B}||$$

But, we also know that,

$$||\overrightarrow{B}||=\frac{||\overrightarrow{E}||}{c}$$

Thus, we get

$$||\overrightarrow{S}||=\frac{1}{c\mu_0}||\overrightarrow{E}||^2$$

Given, $||\overrightarrow{E}||=E=10^{-4}V/m$

Hence, on plugin the value we get

$$||\overrightarrow{S}||=2.655\times 10^{-11}W/m^2$$