Question

If a sinusoidal electromagnetic wave with intensity 18 W/m2 has an electric field of amplitude E, then a 36 W/m2 wave of the same wavelength will have an electric field of amplitude?

a. 4E
b. 2 underroot 2E
c. 2E
d. underroot E

Answer 1

The correct option is D

Step-by-step explanation:

From the question we are told that

The intensity of the first electromagnetic wave is
`I = 18 \ W/m^2`

The amplitude of the electric field is
`E_(max)_1 =A`

The intensity of the second electromagnetic wave is
`I = 36 \ W/m^2`

Generally the an electromagnetic wave intensity is mathematically represented as

`I = (1)/(2) * \epsilon_o * c * E_(max)^2`

Looking at this equation we see that

`I \ \ \alpha \ \ E^2_(max)`

=>
`(I_1)/(I_2) = [ ( E_(max)_1)/( E_(max)_2) ] ^2`

=>
`E_(max)_2 = \sqrt{(x)/(y) } * E_(max)_1`

=>
`E_(max)_2 = \sqrt{(36)/(18) } * E`

=>
`E_(max)_2 = √(2 ) E`