From a local TV station transmitter, a sinusoidal, plane electromagnetic wave is normally incident on an open window that has an area of 0.510 m2. The wave travels to the right in the positive x-direction at the speed of light c and the window is thus perpendicular to the x-axis. See the schematic. Suppose the three electric field components have wave functions: EX = 0 EY = Emsin(kx-ωt) EZ = 0 See the axes below. At the moment shown the electric field - indicated by the vertically upward arrow - points in the positive y direction. Assume the field magnitude Em = 0.01000 V/m. The Erms (root mean square) of the electric field would thus be Erms = 0.00707 V/m. (a) At the moment shown above, in what direction does the magnetic field point? Indicate this direction by drawing a symbol near the z-axis. Compute the numerical value of amplitude Bm of the magnetic field component pointing in the direction you found. (b) Write the wave function for the magnetic field component you referenced in part (a) in terms of Bm, k, ω, t, x, and other symbols. (c) How much energy does this wave carry through the window during 35.0 second TV commercial? Do you need the value of the magnetic field magnitude to answer this question? Explain.

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From a local TV station transmitter, a sinusoidal, plane electromagnetic wave is normally incident on an open window that has an area of 0.510 m². The wave travels to the right in the positive x-direction at the speed of light c and the window is thus perpendicular to the x-axis. See the schematic.

Suppose the three electric field components have wave functions:

E_X= 0

E_Y = E_msin(kx-ωt)

E_Z = 0

See the axes below. At the moment shown the electric field - indicated by the vertically upward arrow - points in the positive y direction. Assume the field magnitude E_m = 0.01000 V/m. The E_rms (root mean square) of the electric field would thus be E_rms = 0.00707 V/m.

(a) At the moment shown above, in what direction does the magnetic field point? Indicate this direction by drawing a symbol near the z-axis. Compute the numerical value of amplitude B_m of the magnetic field component pointing in the direction you found.

(b) Write the wave function for the magnetic field component you referenced in part (a) in terms of B_m, k, ω, t, x, and other symbols.

(c) How much energy does this wave carry through the window during 35.0 second TV commercial? Do you need the value of the magnetic field magnitude to answer this question? Explain.

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