A traveling electromagnetic wave in a vacuum has an electric field amplitude of 59.3 V/m. Calculate the intensity S of this wave. Then, determine the amount of energy U that flows through area of 0.0225 m 2 over an interval of 12.3 s, assuming that the area is perpendicular to the direction of wave propagation.

A) Intensity = 4.664 W/m²

B) U = 1.29J

Explanation:

A) The intensity of the wave is related to a time-averaged version of a quantity called the Poynting vector, and is given by the formula:

I = (E_rms/cμo)

Where;

c = speed of light which has a value of 3 x 10^ (8) m/s

μo = permeability of free space which has a constant value of 4π x 10^ (-7) N/A²

E_rms is root mean square value of electric field

In the question, we are given maximum amplitude of the electric field. In this case, we would have to calculate the "root-mean-square" or "rms" value through the relationship:

E_rms = E_max/√2

Thus, E_rms = 59.3/√2 = 41.93 V/m

Thus, Intensity, I = (E_rms/cμo) = [41.93² / (3 x 10^ (8) x 4π x 10^ (-7)) ]

I = 4.664 W/m²

B) The formula for the energy flowing is given by the formula;

U = IAt

Where;

I is intensity

A is area

t is time in seconds

Thus, U = 4.664 x 0.0225 x 12.3 = 1.29J

Answer: S = 4.67 W/m², U = 1.29 J

Explanation:

Given

Time of flow, t = 12.3 s

Area of flow, a = 0.0225 s

Amplitude, E = 59.3 V/m

Intensity, S = ?

I = E² / cμ, where

μ = permeability of free space

c = speed of light

E = E (max) / √2

E = 59.3 / √2

E = 41.93 V/m

I = 41.93² / (2.99*10^8 * 1.26*10^-6)

I = 1758.125 / 376.74

I = 4.67 W/m²

Energy that flows through

U = Iat

U = 4.67 * 0.0225 * 12.3

U = 1.29 J

Therefore, the intensity is 4.67 W/m² and the energy is 1.29J