Answer to Question #89923 in Electricity and Magnetism for Shivam Nishad

Question

The electric field of a plane electromagnetic wave is given by
Ex = 0, Ey =100 cos(4π x 10^8 t — πX/3)
Ez = 0 where E is in Vm^-1, t is in seconds and x is in meters.
Determine v, k, X, direction of propagation of the wave and the direction of the magnetic field.

Answer 1

Formula for electric field of a plane EM wave

$$E=E_0 \cos(\omega t - \vec{k}\cdot \vec{r})$$

So,

$$|k| = \frac{\pi}{3}\,\text{m}^{-1}$$

is the wavevector, with direction along x-axis:$\vec{k} = (|k|,0,0)$

$$\omega = 4\pi10^8\, \text{s}^{-1}$$

is the frequency of the wave.

As

$$\vec{k} = [\vec{E}\text{x}\vec{B}]$$

Therefore B has only z component only - magnetic field directed along z axis.