Q: When a magnet picks up paperclips or repels/attracts another magnet, work is being done. Working against gravity or friction must use energy. Can someone please explain in words rather than mathematics where the energy comes from and whether a magnet in use (such as one holding notes to a refrigerator door) gradually becomes weaker as its magnetism is used by supporting itself against gravity?
A: There are three pieces of information which you need:
1. (The answer you wanted.) When a stationary magnet picks up a paperclip, energy is being conserved because work is done against the force of gravity by virtue of a reduction in the potential energy of the total global magnetic field.
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2. A magnet on a fridge door is performing no work (work equals force multiplied by distance) and therefore no energy is expended. If the surface is vertical, the vertical holding force is friction, not magnetism.
The magnet will usually become weaker, as its magnetisation slowly becomes more random over time.
The following answers are an elaboration of the three points made above 鈥� Ed.
A: Work is being done when a magnet lifts something, or attracts and repels another magnet, but the source of the energy depends on exactly what is being done. If a magnet is used to lift a paperclip, or to push another magnet away, the work is done by the hand that moves the magnet, rather than by the magnet itself. If the magnet is stationary on a fridge door, no work is being done at all. The position of the magnet with respect to the door (for the force produced by the magnet) or the ground (for the force of gravity) must change for energy to be lost or gained.
If the magnet is attracting something from a distance, work is being done by the magnet itself, but this attraction reduces the free energy of the system, something that everything in the Universe is perpetually trying to do. It turns out that the magnet can lower the total free energy of the system if it pulls something that is easy to magnetise, like a paperclip or a piece of iron, closer to it. The loss of free energy is equal to the work done by bringing the paperclip closer to the magnet. (But the energy is lost by the system, not by the magnet itself. If someone moved the paperclip back to its original position, the free energy of the system would be increased again.) The strength of the force produced by the magnet falls off rapidly with distance, while gravity is an essentially constant force at or near the Earth鈥檚 surface. As a result, a magnet must be placed relatively close to a paperclip to pick it up against the force of gravity. The weaker the magnet is the closer it must be.
A magnet on a refrigerator door will not become weaker over time, but certain types of metal magnets do if they are not attached to a magnetic objects 鈥� they reduce their total energy by developing a return path for the magnetic field inside themselves, and lose their external magnetic field.
A: The writer is correct to assume that work is done and energy is lost (or, more correctly, converted) when an iron object moves under the attraction of a magnet. Magnetism, though, is not energy, it is a force and is not depleted by the work done. As to where the energy comes from or goes to, consider this analogy.
When a stone falls into a hole in the ground, gravity is not weakened in any way. Work has been done by the stone and it has lost some potential energy. If the stone were to be lifted back out of the hole, work would have to be done by the mover which would lose energy and the stone would regain potential energy to its original level.
In the same way, a magnet/iron object system has a level of potential energy which drops as one falls towards the other. The level of potential energy will be restored if energy is put back into the system by an outside agent using energy to do work pulling them apart.
Finally, the magnet will not weaken by supporting itself against gravity since the system is in equilibrium. This may be likened to two forces balanced on a seesaw, neither of which weakens with time. Th corollary is also true: gravity will not be weakened by millions of refrigerator magnets holding themselves up against its force.
A magnet stuck on the refrigerator door will retain its magnetism longer than one on the kitchen floor since the metal door acts as a keeper.
A: Individual atoms of ferro-magnetic elements such as iron, nickel and cobalt possess small magnetic fields due to the net spin of their electrons 鈥� and also they can interact with neighbouring atoms in a way that favours an alignment of spin. Permanent magnets are generally made from some or all of these three elements.
In an unmagnetised sample of a ferromagnetic alloy, the fields of the atoms are aligned over microscopic regions called magnetic domains. These domains are all magnetised in different directions and their combined fields cancel out in a macroscopic sample containing billions of domains. Permanent magnets are created by applying a strong external field which aligns all the atoms in all the domains. This requires a net input of energy, stored in the total magnetic field.
When a permanent magnet lifts a paperclip against gravity, the field of the magnet aligns the random atomic fields of the paperclip, magnetising it. Most of this induced magnetism will be temporary, but some of it will be permanent. Depending on its composition, the paperclip might retain a field of its own which is strong enough to pick up other paperclips.
So the energy stored in the original magnet is dissipated, not because of any work done against gravity (which is simply converted into potential energy), but because work is done by magnetising the paperclip. If a permanent magnet is used repeatedly to magnetise other objects, it must gradually become weaker. A permanent magnet which sticks to a fridge does no work, beyond the initial magnetisation of the fridge door which allows it to stick. On a long enough time scale, it will lose its magnetisation from thermal effects randomising the atomic spins 鈥� but no faster than an equivalent magnet on top of the fridge.