How Can Magnetic Fields Interfere?

         It’s obvious whether we can also treat magnetic fields as a common wave. As doubtlessly known, two propagated waves can be interfered each other.  Wave interference is the phenomenon that occurs when two waves meet while traveling along the same medium. The interference of waves causes the medium to take on a shape resulted from the net effect of the two individual waves upon the particles of the medium.

        Consider two waves that are in phase, sharing the same frequency and with amplitudes A₁ and A₂. Their troughs and peaks line up and the resultant wave will have amplitude A = A₁ + A₂. This is known as constructive interference. If the two waves are π radians, or 180°, out of phase, then one wave's crests will coincide with another waves' troughs and so will tend to cancel it out. The resultant amplitude is A = |A₁ − A₂|. If A₁ = A₂, the resultant amplitude will be zero. This is known as destructive interference.

         When two sinusoidal waves superimpose, the resulting waveform depends on the frequency (or wavelength) amplitude and relative phase of the two waves. If the two waves have the same amplitude A and wavelength the resultant waveform will have amplitude between 0 and 2A depending on whether the two waves are in phase or out of phase.

        A magnetic field is a field of force produced by moving electric charges, by electric fields that vary in time, and by the 'intrinsic' magnetic field of elementary particles associated with the spin of the particle. As a field of force, magnetic field has both direction and amplitude as a common wave has. But, magnetic field’s direction is different with common wave. In term of magnetism, a magnet, source of magnetic field, has an entity called magnetic moment.

        The sources of magnetic moments in materials can be represented by poles in analogy to electrostatics. Consider a bar magnet which has magnetic poles of equal magnitude but opposite polarity. Each pole is the source of magnetic force which weakens with distance. Since magnetic poles always come in pairs, their forces partially cancel each other because while one pole pulls, the other repels. This cancellation is greatest when the poles are close to each other i.e. when the bar magnet is short. The magnetic force produced by a bar magnet, at a given point in space, therefore depends on two factors: on both the strength p of its poles, and l on the vector separating them. The moment is defined as u = pl.
 

        A longitudinal wave from a point source propagates in all direction until its energy runs out. But, magnetic field with the possession of magnetic moment, the direction always comes from “+” poles (north pole) to “–“poles (south pole), called magnetic field lines. This phenomenon is just like a flow, a wave flow acting on magnetic field. So, can we categorize magnetic field as a wave? It becomes interesting question since there is diversity in similarity.

        Interference and diffraction are specific characters of a wave, especially light wave. Double slit experiment by Young has shown those phenomena. Does it happen to magnetic field? If we place 2 magnet bar by parallel mounting with the same pole side to side (analogy of Young’s experiment reconstruction), the magnetic field contour can be described as follow:

        There is no such superposition, but changing in flux density and field intensity in middle region between those magnets. “Magnetic field waves” do not construct or destruct each other, since they have no phase. This changing can be said as interference effect of magnetic field.