Question 15

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by $$E_x = E_0 \sin(kz - \omega t)$$ and $$B_y = B_0 \sin(kz - \omega t)$$. Then the correct relation between $$E_0$$ and $$B_0$$ is given by

$$\nabla \times \vec{E} = -\frac{\partial \vec{B}}{\partial t}$$

$$(\nabla \times \vec{E})_y = -\frac{\partial E_x}{\partial z} = -E_0 k \cos(kz - \omega t)$$

$$-\frac{\partial B_y}{\partial t} = -B_0 (-\omega) \cos(kz - \omega t) = B_0 \omega \cos(kz - \omega t)$$

$$-E_0 k \cos(kz - \omega t) = B_0 \omega \cos(kz - \omega t)$$

$$E_0 k = B_0 \omega$$ (taking magnitude)

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