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For an electromagnetic wave traveling through space, the electric field is given by E = E0 * sin(ky) * sin(omega*t) (in the z-direction). Find the corresponding magnetic field B in space. [c = speed of light in vacuum]

1. (E0/c) * sin(ky) * sin(omega*t) in i-hat direction
2. -(E0/c) * sin(ky) * sin(omega*t) in i-hat direction
3. (E0/c) * cos(ky) * cos(omega*t) in i-hat direction
4. -(E0/c) * cos(ky) * cos(omega*t) in i-hat direction

Correct answer: (E0/c) * cos(ky) * cos(omega*t) in i-hat direction

Solution

Using Faraday's law, (curl E)ₓ = dEz/dy = E0*k*cos(ky)*sin(omega*t) = -dBx/dt. Integrating: Bx = (E0/c)*cos(ky)*cos(omega*t), so B = (E0/c)*cos(ky)*cos(omega*t) i-hat.

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