1) A sinusoidal electromagnetic wave from a radio station passes perpendicularly

Question

1) A sinusoidal electromagnetic wave from a radio station passes perpendicularly through an open window that has area of 0.450 m2 . At the window, the electric field of the wave has an rms value 2.60×102 V/m . How much energy does this wave carry through the window during a 30.0s commercial?

2) He-Ne lasers are often used in physics demonstrations. They produce light of wavelength 633 nm and a power of 0.450 mW spread over a cylindrical beam 1.20 mm in diameter (although these quantities can vary). What is the average energy density in the laser beam?

Explanation / Answer

1) W = 2Atc(0.5*e0*E^2) = 2*0.45*30*3*10^8(0.5*8.85*10^-12*2.6*2.6*10^-4) = 2.42*10^-5 J

Remember, half of the energy in an EM wave is in the E field, the rest is in the B field. Thus, multiply E field energy by 2

2) I = P/A (power/area) = 0.450x10^-3W/(*(0.60x10^-3m)^2 = 397.9 W/m^2

I = Emax^2/(2µo*c) so

Emax = sqrt(2µo*c*I) = sqrt(2*4x10^-7*3.00x10^8*397.9) = 547.7 V/m

u = o*E^2 = 8.85x10^-12*547.7^2 = 2.66 x10^-6 J/m^3

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