Question

Find the intensity of an electromagnetic wave having a peak magnetic field strength of $\mathbf{4}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{9}}\mathbf{T}$.

Short answer

The intensity is$1.91\times {10}^{-3}\mathrm{W}/{\mathrm{m}}^2$ .

Step-by-step solution

Define electromagnetic waves

Electromagnetic waves are waves that are produced by changes in the electric and magnetic fields.

Evaluating the intensity of an electromagnetic wave

The intensity in terms of magnetic field strength is

$I_{avg}=\frac{c{B}_0^2}{2\mu 0}$

Where${\mathrm{I}}_{\mathrm{avg}}$ is average intensity and c is light speed.

Substitute the values in the above equation,

$$\begin{gathered} {\mathrm{I}}_{\mathrm{avg}}=\frac{\left(3\times {10}^8\mathrm{m}/\mathrm{s}\right){\left(4\times {10}^{-9}\mathrm{T}\right)}^2}{2\times 4\mathrm{\tau \tau }\times {10}^{-7}\mathrm{T}\times \mathrm{m}/\mathrm{A}} \\ =1.91\times {10}^{-3}\mathrm{W}/{\mathrm{m}}^2 \\ \mathrm{Therefore},\mathrm{the}\mathrm{intensity}\mathrm{is}1.91\times {10}^{-3}\mathrm{W}/{\mathrm{m}}^2. \end{gathered}$$