Question

Under what conditions do the following
time-varying electric and magnetic fields
satisfy Maxwell's equations in vacuum with
no source charges or currents ?
E = k E0 sin (y - vt)
B = I B0 sin (y - vt)
where E0 and Bo are constants.

Answer 1

These field must satisfy Maxwell equations. For instance, it must satisfy:

$$curl{\vec{E}}=-\frac{d\vec{B}}{dt}$$

It gives:

$$-E_0*cos(y-vt)*\hat{i}=-B_0*v*cos(y-vt)\hat{i}$$

So:

$$v=c=\frac{E_0}{B_0}$$

As we know that the speed of propagation of EM wave equals to the speed of light (c)