Answer:
a) w / k = c
, b) λ = 1,887 10⁻¹ m
, = 4.42 10⁻⁴ J / m³
Explanation:
a) Maxwell's equations when solved for an electromagnetic wave result in
E = E₀ cos (kx - wt)
B = B₀ cos (kx -wt)
Where k is the vector ce wave and w the angular velocity
k = 2π / λ
w = 2π f
Let's divide the two equations
w / k = f λ
w / k = c
Therefore, for w and k to be a solution to Maxwell's equations, their relationship must be equal to the speed of light.
b) If w = 10¹⁰ s⁻¹
w = 2π f
f = w / 2π
f = 10¹⁰ / 2π
f = 1.59 10⁹ Hz
The speed of light is
c = λ f
λ = c / f
λ = 3 10⁸ / 1.59 10⁹
λ = 1,887 10⁻¹ m
Energy density is
= ½ ε₀ E₀²
= ½ 8.85 10⁻¹² (10 10³)²
= 4.42 10⁻⁴ J / m³
Power is energy per unit of time
P = / t
We calculate for every second
P = 4.42 10⁻⁴ W / m³
The flow or intensity of energy is
I = S = c u
I = 3. 108 4.42 10⁻⁴
I = 1.33 10⁵ W / m2
