Question

The oscillatory electric field, of an em wave, propagating along the + z–axis, is represented by E_x = E₀ sin (kz - ωt)

This em wave is incident on a perfectly black circular disc, of diameter d and height h, located parallel to the x–y plane. The total energy absorbed by this surface, over one complete cycle of this em wave, would equal

(1) \((\frac{\pi d^2 hE^2_0}{8μ_0 C^2})\)

(2) \(\frac{\pi d^2hE^2_0}{16c^2}[ε_0 + \frac{1}{c^2μ_0}]\)

(3) \(\frac{\pi d^2hE^2_0}{4c^2}[ε_0 + \frac{1}{c^2μ_0}]\)

(4) \((\frac{\pi d^2 hE^2_0}{8ε_0 C^2})\)

Answer 1

 (1) \((\frac{\pi d^2 hE^2_0}{8μ_0 C^2})\)

We know that

(Volume) energy density of electric field = 1/2

(Volume) energy density of magnetic field = 1/2 \((\frac{B^2}{μ_0})\)

The energy of the EM wave is shared equally between the electric and the magnetic fields. 

Over one complete cycle, we need to use E_rms and B_rms in the above expressions.

∴ Total energy delivered over one complete cycle