Question

The electrical breakdown in air occurs at electric field strength of 3.5MV/m
.
Calculate the corresponding intensity of a plane wave.

Answer 1

We can find the corresponding intensity of a plane wave from the formula:

$$I = \dfrac{1}{2}c\epsilon_0E^2,$$

here, $c = 3 \cdot 10^8 m/s$ is the speed of light, $\epsilon_0 = 8.85 \cdot 10^{-12} F/m$ is the permittivity of free space and $E = 3.5 \cdot 10^6 V/m$ is the electric field strength.

Finally, we can calculate the corresponding intensity of a plane wave:

$I=\dfrac{1}{2} \cdot 3 \cdot 10^8 \dfrac{m}{s} \cdot 8.85 \cdot 10^{-12} \dfrac{F}{m} \cdot (3.5 \cdot 10^6 \dfrac{V}{m})^2 = 1.63 \cdot 10^{10} \dfrac{W}{m^2}.$

Answer:

$I = 1.63 \cdot 10^{10} \dfrac{W}{m^2}.$