Question

Please help me, i'll give u medal..
a sinusoidal electromagnetic wave with a frequency of 1.5x 10 ^ 15 Hz propagates in vacuum in the positive y-axis direction. Magnetic field is parallel to the x axis with an amplitude of 3 mT. When y = 0 and t = 0, the large magnetic field is 0. Determine the function of the wave vector of the magnetic field and electric field at the time t.

Answer 1

For a travelling wave in vacuum, vectors k, E and B must be at right angles to each other.
\[\vec B(M,t)=\frac{\vec k}{\omega}\times\vec E(M,t)\]
k=ω/c

\[\vec B(M,t)=\vec B(y,t)=B _{0}\:e ^{i(\omega t-ky+\frac{\pi}{2})}\;\vec u _{x}\]where ux is unit vector along x-axis.
π/2 is there in the phase because the problem states that when y=0 and t=0, B=0

You should easily find the expression of E(M,t) using the equations above.