The property which is not of an electromagnetic wave travelling in free space is that:

The correct option is: They originate from charges moving with uniform speed.

To understand why this is correct, let us analyze the origin and properties of electromagnetic waves travelling in free space step-by-step:

1. Source of Electromagnetic Waves:
An electromagnetic wave is a disturbance that propagates through space, carrying electromagnetic radiant energy. According to Maxwell's equations, electromagnetic waves are generated by accelerated or oscillating charges.
- A static charge (velocity = 0) produces only an electric field.
- A charge moving with a constant, uniform speed produces both electric and magnetic fields, but these fields are steady and do not radiate energy into space.
- Only when a charge is accelerated (which includes oscillation) does it continuously produce time-varying electric and magnetic fields that propagate outward as electromagnetic waves. Therefore, electromagnetic waves cannot originate from charges moving with a uniform speed.

2. Transverse Nature:
In an electromagnetic wave, the electric field vector and the magnetic field vector oscillate perpendicular to each other, and both are perpendicular to the direction of propagation of the wave. This makes electromagnetic waves transverse in nature.

3. Equal Energy Density:
In free space, the energy of an electromagnetic wave is shared equally between the electric and magnetic fields. The average energy density of the electric field is equal to the average energy density of the magnetic field.

4. Speed of Electromagnetic Waves:
In free space, electromagnetic waves travel at the speed of light, which is mathematically expressed using the permittivity of free space ${\epsilon }_0$ and the permeability of free space ${\mu }_0$ as:

$c=\frac{1}{\sqrt{{\mu }_0{\epsilon }_0}}$

Thus, the statement that they originate from charges moving with uniform speed is incorrect, making it the property that does not belong to an electromagnetic wave.