Question

A plane electromagnetic wave has a maximum electric field magnitude of$\mathbf{3}\mathbf{.}\mathbf{20}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{4}}\mathbf{}\mathbf{\text{V/m}}$. Find the magnetic field amplitude.

Short answer

The magnetic field amplitude is $1.067\times {10}^{-12}\mathrm{T}$.

Step-by-step solution

Listing the given quantities

Maximum electric field magnitude $E_m=3.20\times {10}^{-4}\text{V/m}$.

Understanding the concepts of magnetic field

The electric $E_m$and magnetic fields $B_m$are related to the wave speed c as,

$c=\frac{E_m}{B_m}$

Calculations of the magnetic field amplitude

The electric and the magnetic field are related as,

$c=\frac{E_m}{B_m}$

Where c is the wave speed $c=3.0\times {10}^8\text{m/s}$.

Rearranging the above expression as,

$B_m=\frac{E_m}{c}$

Substitute the values in the above expression, and we get,

$\begin{array}{rcl}{B}_m& =& \frac{3.20\times {10}^{-4}\text{V/m}}{3.0\times {10}^8\text{m/s}}\\ & =& 1.067\times {10}^{-12}\mathrm{T}\end{array}$

Thus, the magnetic field amplitude is $1.067\times {10}^{-12}\mathrm{T}$.