It can be shown from Maxwell's equations that electric and magnetic fields in an electromagnetic wave are perpendicular to each other, and to the direction of propagation.

If electric field `E_x` is along the x-axis, and varies sinusoidally with z, at a given time. The magnetic field `B_y` is along the y-axis, and again varies sinusoidally with z. The electric and magnetic fields `E_x` and `B_y` are perpendicular to each other, and to the direction z of propagation.

We can write `E_x` and `B_y` as follows :

`E_x= E_0 sin (kz-ωt )....(1)`
`B_y= B_0 sin (kz-ωt ).....(2)`

Here `k=(2pi)/lamda` is the magnitude of the wave vector (or propagation vector).
`ω` is the angular frequency.

The speed of propagation of the wave is `omega/k`.

Using Eqs. (1) and (2) for `E_x` and `B_y` and Maxwell's equations, one finds that

`omega=ck` where `c=1/sqrt(mu_0epsilon_0)` `......(3)`

In terms of frequency `nu=omega/(2pi)` and wavelength `lamda= (2pi)/k`
as, `2pinu=c((2pi)/lamda)`
`nulamda=c.....(4)`

It is also seen from Maxwell's equations that the magnitude of the electric and the magnetic fields in an electromagnetic wave are related as `B_0=(E_0)/c`

`text(We here make remarks on some features of electromagnetic waves :)`

`=>` They are self-sustaining oscillations of electric and magnetic fields in free space, or vacuum.
`=>` They differ from all the other waves we have studied so far, in respect that no material medium is involved in the vibrations of the electric and magnetic fields.
`=>` Transverse waves on the surface of water consist of water moving up and down as the wave spreads horizontally and radially onwards.
`=>` Transverse elastic (sound) waves can also propagate in a solid, which is rigid and that resists shear.

Electric and magnetic fields, oscillating in space and time, can sustain each other in vacuum.

The velocity of electromagnetic waves in free space or vacuum is an important fundamental constant.