Question

Ex. 7.1 — The radiation pressure from the sun at the surface of the earth is only 6 uPa. Calculate the RMS amplitude of the electric field component of a monochromatic electromagnetic wave that would exert such a pressure. (Monochromatic = single frequency).

Answer 1

Answer:

Radiation pressure P in terms of the intensity of the electromagnetic wave I is P = I/c ---------- (1), where c is speed of light.

Now, the intensity of EM wave I = E_RMS B_RMS/ μ₀ ---------- (2)

and the relation between E_RMS and B_RMS isB_RMS = E_RMS/c ---------- (3)

Substitute Eq.(3) in Eq.(2), then we obtains,

I = (E_RMS/ μ₀) B_RMS = (E_RMS/ μ₀) (E_RMS/c) = (E_RMS)²/ μ₀c ------ (4)

Then, substitute Eq.(4) in Eq.(1), then we obtain,

P = I/c = (1/c) (E_RMS)²/ μ₀c = (E_RMS)²/ μ₀c²

But c² = 1/μ₀ε₀, therefore

P = [(E_RMS)²/ μ₀] (1/c²) = [(E_RMS)²/ μ₀] [1/(1/μ₀ε₀)] = [(E_RMS)²/ μ₀] (μ₀ε₀) = (E_RMS)² ε₀. ----------- (5)

That means, P = (E_RMS)²ε₀. But we need only the E_RMS therefore E_RMS = [P/ε₀]^1/2 .

Given that radiation pressure P = 6 μPa = 6 x 10^-6 Pa.

Therefore, E_RMS = [(6 x 10^-6 Pa) / (8.85 x 10^-12 C²/Nm²) ]^1/2 = [0.677 x 10⁶ N²/C²]^1/2 = 822.80 N/C.