Question

In a wave $E_0=100V{m}^{-1}$. Find the Poynting vector magnitude.

• A. $13.25W{m}^{-2}$
• B. $26.5W{m}^{-2}$
• C. $18.25W{m}^{-2}$
• D. $19.7W{m}^{-2}$

Answer 1

The correct option is B

$26.5W{m}^{-2}$

Step 1: Given data

$E_0=100V{m}^{-1}$

Step 2: Formula used

$\left|\overrightarrow{s}\right|=\frac{{E_0}^2}{c{\mu }_0}$

Where $\overrightarrow{s}$ is the Poynting vector, $E_0$ is the electric field, $c$ is the speed of light and ${\mu }_0$ is the permeability.

Step 3: Finding the magnitude of the Poynting vector

We know the magnitude of the Poynting vector,

$$\begin{gathered} \left|\overrightarrow{s}\right|=\frac{{E_0}^2}{c{\mu }_0} \\ \Rightarrow \left|\overrightarrow{s}\right|=\frac{{100}^2}{3\times {10}^8\times 4\mathrm{\pi }\times {10}^{-7}} \\ \Rightarrow \left|\overrightarrow{s}\right|=26.5W{m}^{-2} \end{gathered}$$

The magnitude of the poynting vector is $26.5W{m}^{-2}$.

Hence, option B is correct.