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A plane electromagnetic wave of frequency 500 MHz travels in vacuum along the +y direction. At a certain point in space and time, the magnetic field is B = 8.0*10⁻⁸ z-hat T. Find the electric field at this point. (c = 3*10⁸ m/s; x-hat, y-hat, z-hat are unit vectors along x, y, z.)

1. -24 x-hat V/m
2. 2.6 x-hat V/m
3. 24 x-hat V/m
4. -2.6 y-hat V/m

Correct answer: -24 x-hat V/m

Solution

In an EM wave E0 = c B0 = (3*10⁸)(8.0*10⁻⁸) = 24 V/m. The wave moves along +y, so E x B must be along +y. With B along +z, we need E direction d such that d-hat x z-hat = +y-hat. Testing d = -x-hat: (-x-hat) x (z-hat) = -(x-hat x z-hat) = -(-y-hat) = +y-hat. Correct. So E = -24 x-hat V/m.

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