Respuesta :
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
Answer:
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
