Question

In the $EM$ wave the amplitude of magnetic field $H_0$ and the amplitude of electric field $E_0$ at any place are related as:

• A. $H_0=E_0$
• B. $H_0=\frac{E_0}{c}$
• C. $H_0=E_0\sqrt{\frac{{\mu }_0}{{\in }_0}}$
• D. $H_0=E_0\sqrt{\frac{{\in }_0}{{\mu }_0}}$

Answer 1

The correct option is B $H_0=\frac{E_0}{c}$

We know that

$\frac{AmplitudeoftheelectricfieldofFMwave}{Amplitudeofthemag.FieldofsameFMwave}=\left(speedoflightinvacuum\right)$

$\Rightarrow$ Given that

Amplitude of electric field $=E_0$

Amplitude of magnetic field$=H_0$

Speed of light in vacuum $=c$

Hence, $\frac{E_0}{H_0}=c$

$\Rightarrow H_0=\frac{E_0}{c}=E_0=\sqrt{{\mu }_0{\epsilon }_0}[\because c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}]$

$\Rightarrow$ option $B$