Question

The electromagnetic wave that delivers a cellular phone call to a car has a magnetic field with an rms value of 1.90 10-10 T. The wave passes perpendicularly through an open window, the area of which is 0.20 m2. How much energy does this wave carry through the window during a 35-s phone call?

Answer 1

The energy flux (or intensity) of plane electromagnetic wave is equal to the time averaged magnitude of the Poynting vector,
I = (ε₀∙c/2)∙ E₀² = (µ₀∙c/2)∙ B₀²
where
ε₀ vacuum permittivity, c speed of light, E₀ amplitude ot the electric field, µ₀∙magnetic constant , B₀ amplitude of the magnetic field

For this wave
I = <S> = (µ₀∙c/2)∙ B₀²
= (4π×10⁻⁷Tm/A ∙ 2.998×10⁸m/s / 2)∙ (1.2×10⁻¹⁰ T)²
= 5.425×10⁻¹⁸J/m²s

Multiply this by the area and the time and you have the energy you are looking for:
E = I ∙ A ∙t
= 5.425×10⁻¹⁸J/m²s ∙ 0.2m² ∙ 50s
= 5.425×10⁻¹⁷J