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?

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 = = (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