Force Between Magnets Over a Distance

Public domain image via Pixabay

As you probably know, like poles of magnets repel and unlike poles attract. The force between two magnets increases as they're brought closer together, but how does it vary? Many things in nature follow an inverse square law. So the luminous intensity of an omnidirectional (the same in all directions) light source or loudness of an omnidirectional sound source follows an inverse square law. If you move 3 times further away from a sound than your original position, the loudness reduces by a factor of 9. At 100 times the original distance, the loudness reduces by 100 x 100 =10,000 times. Similarly for the brightness of a light. That's because the sound or light flux is passing through an imaginary sphere and the surface area of a sphere depends on the square of its radius (4πr²). In this Quora post, we discover that for a magnet, the scenario is a lot more complicated because fields aren't uniformly shaped.

3D Magnetic Field Visualisation

Ferrofluid following magnetic field lines. Image attribution: Gregory F. Maxwell, CC BY-SA 3.0 via Wikimedia Commons

You probably performed the experiment in primary school where you place a sheet of paper over a bar magnet and sprinkle iron filings, give the sheet a tap, and the particles of iron arrange themselves along the magnetic field lines of the magnet. However the iron filings experiment only visualises a slice through the magnetic field. In fact, magnetic fields are three dimensional and the top photo is a 3D version of the experiment using ferrofluid, a colloidal liquid (like milk or emulsion paint) with a suspension of nanoscale ferromagnetic (influenced by magnetism e.g. iron) particles. The ferrofluid is placed on a sheet of glass above a neodymium magnet.

Iron filings on paper following magnetic field lines of a bar magnet. Image attribution: Newton Henry Black, public domain via Wikimedia Commons

 

Cartoon Capers

Image created using Bing Image Creator

You know those cartoons where Wile E. Coyote uses a giant magnet in one of his ill-fated plots to capture the Road Runner? It‘d be brilliant if such magnets exited, but unfortunately not. Gravity is one of the forces that act at long distances (well strictly gravity is not a proper force, but that's another story), however the force of a magnet is relatively localised to a region close to its north and south poles. So magnets in scrapyards can lift tons of metal, but they have to be lowered until they're nearly touching scrap. If the field strength of a magnet is increased sufficiently, the force can extend outwards some distance, but the force still obeys an inverse square law with respect to distance. So for instance let’s say the distance from a magnet is one cm. The force will have a certain value. At two cm, the force decreases to one quarter that value and at three cm to one ninth the value (nine being the square of three). At four cm, it’ll have fallen to one sixteenth the strength it was at one cm, and so on. To complicate things, force follows an inverse cube law close to a magnet, which causes an initial rapid drop-off in attractive force. Many parameters in nature follow an inverse square law, for example the brightness of an omnidirectional (the same in all directions) light source or the loudness of a sound source as an observer moves away from the source. Gravity also follows an inverse square law and the force of attraction between two bodies is proportional to the product of their masses (Either body being more massive increases the force) and inversely proportional to the square of their distance apart. (all of this discovered by Isaac Newton, the scientist and mathematician). The force of gravity of the Sun on a 70 kg person is about 42 g.