Question

The rms value of the electric field in a certain light waveis$\mathbf{0}\mathbf{.}\mathbf{200}\mathbf{}\mathit{V}\mathbf{/}\mathit{m}$.What is the amplitude of the associated magnetic field?

Short answer

The amplitude of the associated magnetic field is$B_{amp}=9.43\times {10}^{-10}T$

Step-by-step solution

Listing the given quantities 

$E_{rms}=0.200V/m$

Understanding the concepts of magnetic field

By using the relation between the magnitude of the electric field andthe magnitude of the magnetic field, given by equation$\mathbf{33}\mathbf{-}\mathbf{5}$ ,we can find the magnetic field.

Formula:

$\frac{E}{B}=C$

$B_{rms}=\frac{B_{amp}}{\sqrt{2}}$

Calculations of theamplitude of the associated magnetic field

By using the equation,$33-5$we have,

$\frac{E}{B}=C$

where C is the velocity of the electromagnetic wave, which is$3\times {10}^{8}m/s$.

Rearranging the equation, we can find the rms magnetic field,

$\begin{array}{c}{B}_{rms}=\frac{E_{rms}}{C}\\ =\frac{0.200}{3\times {10}^8}\\ =6.67\times {10}^{-10}T\end{array}$

This is the value of the magnetic field. To find the amplitude of the magnetic field, we can multiply this value by $\sqrt{2}$.

$\begin{array}{c}{B}_{rms}=\frac{B_{amp}}{\sqrt{2}}\\ B_{amp}=B_{rms}\sqrt{2}\\ =6.67\times {10}^{-10}\times \sqrt{2}\\ =9.43\times {10}^{-10}T\end{array}$

Hence, the amplitude of the associated magnetic field is$B_{amp}=9.43\times {10}^{-10}T$