Question

The ratio of $\frac{E_0}{H_0}$ for a plane electromagnetic wave has the dimension of-

• A. Impedance
• B. Resistance
• C. (a) and (b) above.
• D. None of the above

Answer 1

The correct option is C (a) and (b) above.

As we know, the relation between magnetic field$\left(B\right)$ and intensity of magnetic field$\left(H\right)$ is given by,

$B=\mu H$

In vaccum, $B_0={\mu }_0{H}_0.....\left(1\right)$

Also, $\frac{E_0}{B_0}=c$

For vacuum, we can rewrite this equation as,

$B_0={\mu }_0{H}_0.......\left(i\right)$

Relation between magnetic field and electric field for vacuum is given as,

$B_0={\mu }_0{\epsilon }_{0}c{E}_0.......\left(ii\right)$

From equations (i) and (ii)

${\mu }_0{H}_0={\mu }_0{\epsilon }_{0}c{E}_0$

$\Rightarrow \frac{E_0}{H_0}=\frac{1}{{\epsilon }_{0}c}$

And dimension of above equation, $\left[\frac{E_0}{H_0}\right]$ is Ohm.