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?
Multiply the Poynting flux vector S by the window area and the 35 s time interval.
You will need an electromagnetism textbook to relate the Poynting (energy) flux to the rms B field. S is proportional to the square of the B field.
S (W/m^2) = 2*[10^7 c/(8 pi)]*Brms(T)^2
If B = 1.9*10^-10 T, the electromegnetic flux is
S = 2.38*10^14*Brms^2
= 8.6*10^-6 W/m^2
Energy = 6.02*10^-5 W
To calculate the energy carried by the electromagnetic wave through the window during a phone call, we can use the formula:
Energy = Power x Time
First, we need to calculate the power of the wave passing through the window. The power of an electromagnetic wave can be calculated using the formulas:
Power = (1/2) x ε₀ x c x E₀^2
where ε₀ is the permittivity of free space (8.85 × 10^-12 C^2/Nm^2) and c is the speed of light (3.00 × 10^8 m/s).
Given that the magnetic field has an rms value (E₀) of 1.90 × 10^(-10) T, we can calculate the power as follows:
Power = (1/2) x (8.85 × 10^-12 C^2/Nm^2) x (3.00 × 10^8 m/s) x (1.90 × 10^(-10) T)^2
Next, we can multiply the power by the duration of the phone call (35 s) to give us the energy:
Energy = Power x Time
Finally, we can substitute the calculated power and time into the formula to get the energy:
Energy = [calculated Power] x 35 s
Calculating the values gives us the energy carried by the wave through the window during the phone call.