The implication of electromagnetic waves having momentum, as described by Maxwell's equations, is that they can exert a force on objects they interact with. This phenomenon is known as radiation pressure or electromagnetic radiation pressure.
According to Maxwell's equations, changing electric and magnetic fields can generate propagating electromagnetic waves. These waves carry both energy and momentum. The momentum of an electromagnetic wave is directly proportional to its energy and the direction of propagation. The momentum density (momentum per unit volume) of an electromagnetic wave is given by the equation:
P = (1/c^2) * E x B
where P is the momentum density, E is the electric field vector, B is the magnetic field vector, and c is the speed of light.
When an electromagnetic wave interacts with an object, it imparts its momentum to that object. The momentum transfer can result in a force exerted on the object. This force is proportional to the intensity of the electromagnetic wave (related to the amplitude of the electric and magnetic fields) and the area over which the wave is incident on the object.
The radiation pressure from electromagnetic waves can have practical applications. For example, in optical tweezers, focused laser beams are used to trap and manipulate microscopic particles by exerting radiation pressure on them. Additionally, the radiation pressure from sunlight is responsible for the momentum transfer to spacecraft, which can be utilized for solar sails and other propulsion mechanisms.
Overall, the recognition that electromagnetic waves carry momentum allows us to understand and utilize the force they exert on objects, leading to various scientific and technological applications.