The ratio of the magnitude of the magnetic field and electric field intensity of a plane electromagnetic wave

Question

The ratio of the magnitude of the magnetic field and electric field intensity of a plane electromagnetic wave in free space of permeability $\mu_0$ and permittivity $\varepsilon_0$ is: (Given that $c=$ velocity of light in free space)

Accepted Answer

1. **Relationship between E and B:** In a plane electromagnetic wave propagating in free space, the ratio of the magnitude of the electric field ($E_0$) to the magnitude of the magnetic field ($B_0$) is equal to the speed of light ($c$).
   $$c = \frac{E_0}{B_0}$$
   (Reference: NCERT Class 12, Physics Part I, Chapter 8, Section 8.3).
2. **Ratio Asked:** The question asks for the ratio of the magnetic field to the electric field ($\frac{B_0}{E_0}$).
3. **Calculation:** Rearranging the standard formula:
   $$ \frac{B_0}{E_0} = \frac{1}{c} $$
4. **Additional Context:** Since the speed of light is also defined as $c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}}$, the ratio could also be expressed as $\sqrt{\mu_0 \varepsilon_0}$, but $\frac{1}{c}$ is the option provided.

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