The equation of the electric field of an electromagnetic wave propagating through free space is given by :
E = √377 sin(6.27 × 10³t - 2.09 × 10⁻⁵x) N/C
The average power of the electromagnetic wave is (1/α) W/m². The value of α i $s _______$
(Take √(μ₀/ε₀) = 377 in SI units)

Question

The equation of the electric field of an electromagnetic wave propagating through free space is given by :

E = √377 sin(6.27 × 10³t - 2.09 × 10⁻⁵x) N/C

The average power of the electromagnetic wave is (1/α) W/m². The value of α i $s _______$

(Take √(μ₀/ε₀) = 377 in SI units)

G1 Physics · Accepted Answer

The wave has electric-field amplitude E₀ = √377 N/C. For a plane electromagnetic wave in free space, the average intensity can be written as I(avg) = E₀²/(2Z₀), where Z₀ = √(μ₀/ε₀) = 377 Ω. Therefore, I(avg) = 377/(2×377) = 1/2 W/m². The question writes the average power per unit area as 1/α W/m². Hence, 1/α = 1/2. Therefore, α = 2.

The equation of the electric field of an electromagnetic wave propagating through free space is given by : E = √377 sin(6.27 × 10³t - 2.09 × 10⁻⁵x) N/C The average power of the electromagnetic wave is (1/α) W/m². The value of α i s _______ (Take √(μ₀/ε₀) = 377 in SI units)