Electromagnetic waves have several defining characteristics when they propagate through free space. Let's evaluate each of the options provided:

Option A: They are transverse in nature.

This is true. Electromagnetic waves are transverse waves, meaning the directions of the electric field and magnetic field oscillations are perpendicular to the direction of wave propagation. The electric field (E) and magnetic field (B) vectors are also perpendicular to each other and to the direction of propagation.

Option B: The energy density in the electric field is equal to the energy density in the magnetic field.

This is also true. In electromagnetic waves, the energy density stored in the electric field is equal to the energy density stored in the magnetic field. This is because the magnitudes of the electric and magnetic fields are related by $ c = \frac{E}{B} $ where c is the speed of light in vacuum. The energy density for each is given by $$\frac{1}{2} \epsilon_0 E^2 $$ for the electric field and $$\frac{1}{2} \frac{B^2}{\mu_0}$$ for the magnetic field. Given the relationship between E and B in a wave, these two energy densities are equal.

Option C: They travel with a speed equal to $$\frac{1}{\sqrt{\mu_0 \varepsilon_0}}$$.

This statement is true. The speed of electromagnetic waves in vacuum is given by $$ c = \frac{1}{\sqrt{\mu_0 \varepsilon_0}} $$, where $ \mu_0 $ is the magnetic permeability of free space and $ \varepsilon_0 $ is the electric permittivity of free space. This relationship derives from Maxwell’s equations in a vacuum.

Option D: They originate from charges moving with uniform speed.

This statement is false. Electromagnetic waves are not generally produced by charges moving with a uniform speed; rather, they are produced by charges that are accelerating. Uniform motion (where velocity is constant and acceleration is zero) does not result in radiation of electromagnetic waves. If a charge is accelerating – changing either the speed or direction of its motion – it emits electromagnetic radiation.

Therefore, the correct answer is Option D, as it is the property that is not true for electromagnetic waves traveling in free space.