An electromagnetic wave propagates in the -y direction. If the magnetic field is oriented along the z direction, then what is the orientation direction of the E field?

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The question asks us to find the orientation of the electric field E given a wave propagating in the -y direction and the magnetic field B oriented along +z. In free space, the Poynting vector S ∝ E × B points in the direction of propagation, so E × B must align with -y.

Option 1: E along -z. Compute E × B = (-z) × (+z) = 0, since parallel vectors yield zero cross product. This cannot point in the -y direction, so this choice is incorrect.

Option 2: E along +z. Compute E × B = (+z) × (+z) = 0 for the same reason. A zero cross product cannot indicate propagation direction, so this is also incorrect.

Option 3: E along +x. Compute E × B = (+x) × (+z) = -y. This matches the required propagation direction (-y). Therefore this orientation is consistent with the given k and B, making it a correct choice.

Option 4: E along -x. Compute E × B = (-x) × (+z) = -(x × z) = -(-y) = +y. This yields +y, not the prescribed -y propagation direction, so this is incorrect.

Summarizing, only the +x direction for E yields the correct cross product with B to give propagation in the -y direction, whereas the other options fail either by producing zero or the wrong cross-product direction.

ECEN-322:200,501 Quiz 4

An electromagnetic wave propagates in the -y direction. If the magnetic field is oriented along the z direction, then what is the orientation direction of the E field?

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