Question

If a sinusoidal electromagnetic wave with intensity 20 W/m2 has an electric field of amplitude E, then a 40 W/m2 wave of the same wavelength will have an electric field of amplitude If a sinusoidal electromagnetic wave with intensity 20 has an electric field of amplitude , then a 40 wave of the same wavelength will have an electric field of amplitude 4E . 22√E. 2E. 2√E.

Answer 1

`√(2) E`

Step-by-step explanation:

The intensity of an electromagnetic wave is proportional to the square of the amplitude of the electric field:

`I\propto E^2`

where

I is the intensity

E is the amplitude of the electric field

Therefore, considering the two waves of the problem, we can write:

`(I_1)/(E_1^2)=(I_2)/(E_2^2)`

where

`I_1 = 20 W/m^2` is the intensity of the first wave

`E_1=E` is the electric field amplitude of the first wave

`I_2 = 40 W/m^2` is the intensity of the second wave

`E_2` is the electric field amplitude of the second wave

Solving for
`E_2`,

`E_2 = E \sqrt{(I_2)/(I_1)}=E\sqrt{(40)/(20)}=√(2) E`