Question

I. Representations of electromagnetic waves A. Shown below are mathematical and pictorial representations of an electromagnetic plane wave propagating through empty space. The electric field is parallel to the z-axis; the magnetic field is parallel to the y-axis. .y, and are unit vectors along the x, ty, and +z directions.) 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 points1-4 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, B(x, y, z, t), ahove.

NUMBER 2 only explain clearly

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Answer 1

2. As shown in the figure the electric field is a transverse wave which vibrates in a direction perpendicular to the direction of propagation. Here it vibrates along the z axis and propogates along the X axis. The magnitude of the wave only varies along X axis and is unaffected by any change in z axis. Therefore point 1 and 2 will have same magnitude and point 3 and 4 would have same magnitude. And as seen from the diagram we can say that 1 = 2 > 3 = 4 in terms of magnitude.

Yes it is consistent with the mathematical expression. As changing z would not cause any change but by changing the X the magnitude of the expression will change according to sine wave.

In the same way magnetic field will also vary. Here it vibrates in y direction and propogates in X direction. And as shown we can say 1 = 2 > 3 = 4 magnitude wise. As it is also consistent with its mathematical expression as only change in X causes change in magnitude.