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A plane electromagnetic wave propagates along the positive X-axis with a wavelength of 3 mm. The electric field oscillates in the Y-direction with amplitude 66 V/m. Write the expressions for the electric and magnetic field vectors as functions of position x and time t.

1. Ey = 33 cos(pi * 10¹¹ * (t - x/c)) V/m; Bz = 1.1 * 10⁻⁷ cos(pi * 10¹¹ * (t - x/c)) T
2. Ey = 11 cos(2*pi * 10¹¹ * (t - x/c)) V/m; By = 1.1 * 10⁻⁷ cos(2*pi * 10¹¹ * (t - x/c)) T
3. Ex = 33 cos(pi * 10¹¹ * (t - x/c)) V/m; Bx = 1.1 * 10⁻⁷ cos(pi * 10¹¹ * (t - x/c)) T
4. Ey = 66 cos(2*pi * 10¹¹ * (t - x/c)) V/m; Bz = 2.2 * 10⁻⁷ cos(2*pi * 10¹¹ * (t - x/c)) T

Correct answer: Ey = 66 cos(2*pi * 10¹¹ * (t - x/c)) V/m; Bz = 2.2 * 10⁻⁷ cos(2*pi * 10¹¹ * (t - x/c)) T

Solution

For an EM wave along +X with E along Y, the magnetic field B is along Z (from E x B = propagation direction). Amplitude B0 = E0/c = 66/(3*10⁸) = 2.2*10⁻⁷ T. Angular frequency omega = 2*pi*c/lambda = 2*pi*(3*10⁸)/(3*10⁻³) = 2*pi*10¹¹ rad/s. So E_y = 66 cos(2*pi*10¹¹*(t - x/c)) and B_z = 2.2*10⁻⁷ cos(2*pi*10¹¹*(t - x/c)).

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