Write the relation for the speed of electromagnetic waves in terms of the amplitudes of electric and magnetic fields.

Consider following harmonic electromagnetic wave,
Assume that the electric and magnetic fields are constrained to the y and z directions, respectfully, and that they are both functions of only x and t
E = Em cos(kx - ωt)
B = Bm cos(kx - ωt)
E and B are electric and magnetic fields with amplitudes Em and Bm respectively. k is the wave number and ω is the frequency.
Now Maxwell's equation gives us
∇ × E = -∂B/∂t
The curl of electric field yields
∂E/∂x
^k
∴ ∂E/∂x = -∂B/∂t
Partially differentiating the Electric and Magnetic field equations above.
kEm sin(kx - ωt) = -(-Bmω sin(kx - ωt))
c = ω/k = Em/Bm
where c is phase speed of electro-magnetic waves