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In a plane electromagnetic wave, the electric field points along k (the z-direction) and the magnetic field points along (2i - 2j). Find the unit vector in the direction of propagation of the wave.

1. (i + j)/sqrt(2)
2. (i + 2j)/sqrt(5)
3. (2i + j)/sqrt(5)
4. (j + k)/sqrt(2)

Correct answer: (i + j)/sqrt(2)

Solution

For an EM wave the direction of propagation is along E x B. Taking E along k and B along (2i - 2j), the cross product k x (2i - 2j) = 2j + 2i, which normalises to (i + j)/sqrt(2).

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