You’ve probably heard of Maxwell’s equations, which are a list of four equations that beautifully describe electricity and magnetism. Maxwell’s equations laid the groundwork for a majority of today’s technology that utilises electricity and magnetism, that is radios, wireless communication, motors, engines, generators just to name a few. Each of the four equations are great potential (hahah) blog posts, therefore in this post, I’d be focusing on this one:
Now, as a refresher what do the arrows, dot, B and upside down triangle even mean? B represents the magnetic field, the triangle and the dot together represents something known as “divergence” (we’ll come back to this) and the arrow means that the magnetic field is a vector.
Now, what is “divergence”? To understand divergence, we need to know what a vector field is. A vector field is just a region of space where a certain vector has been assigned to every point in space. A classic example of a vector field is the speed of a fluid moving through space. Sound familiar? Yep, a weather map is a vector field. On weather maps, vectors represent the direction as well as the speed of wind in a particular region of space. As you may have already guessed, B, our magnetic field, can also be represented as a vector field. Here, the vector represents the direction and magnitude of the force experienced by an object capable of feeling the magnetic force at a particular point in space.
Since we now know what a vector field is, we can finally talk about “divergence”. When we’re trying to find the divergence of a vector field, what we’re doing is calculating how much that vector field either points in or out of a very small region of space. If the vector field in a small region of space is ONLY going in (a sink), then the divergence would be negative, and conversely if the vectors are ONLY going out (source), then the divergence would be positive. Now here’s the interesting bit, if an equal number of vectors are going in and coming out, then the divergence of that vector field in that region in space would be zero. Back to Maxwell’s equation. You can now read the equation as “the magnetic field entering and the magnetic field leaving ANY small region of space in a magnetic vector field is always zero.” This is mind blowing. It basically says that every magnet needs to have both a source and a sink. If a magnetic monopole were to exist, the magnetic field entering a region would not be equal to the magnetic field exiting it, and hence violate this equation. This is why you break a bar magnet in half, you always get two poles on each of the broken piece.
Interestingly some newer theories predict the existence of magnetic monopoles. This should not really be a surprise to those who know about the dual nature of light and matter. According to Maxwell’s equations light is only a wave, but recent experiments have challenged that notion. If light can be a wave sometimes and a particle other times, well who knows, maybe you do actually have magnetic monopoles.