Explain step by step. thanks A. Shown below are mathematical and pictorial repre

Question

Explain step by step.

thanks

A. Shown below are mathematical and pictorial representations of an electromagnetic plane wave propagating through empty space. The clectric field is parallel to the -axis; the magnetic field is pairallel to the y-axis. (,y, and 2 are unit vectors along the +x, ty, and +z directions.) E(x, y, z, t) = E,sin(kx + at)2 B(x, y, z. t) = B^ sin(kx + cofjy 1. In which direction is the wave propagating? Explain how you can tell from the expressions for the electric field and magnetic field. Is the wave transverse or longitudinal? Explain in terms of the quantities that are oscillating 2. The points 1-4 in the diagram above lie in the x-z plane For the instant shown, rank these points according to the magnitude of the electric field If the electric field is zero at any point, statc that explicitly Is your ranking consistent with the mathematical expression for the electric field shown above? If not, resolve any inconsistencies. (For example, how, if at all, does changing the value of z affect the value of E(x, y, z, 1)?) For the instant shown, rank points 1-4 according to the magnitude of the magnetic field Check that your ranking is consistent with the expression for the magnetic field, Bix, y, z, ), above.

Explanation / Answer

The wave is travelling in the x-direction because the direction of propagation of an EM wave is always perpendicular to the direction of electric field and magnetic field.

The wave is a transverse wave because the displacement of the magnetic field and the electric field is perpendicular to the direction of propagation of the EM wave.

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