# Doesn't magnetism violate Newton's First Law?

If you place two magnetic objects close to each other, they will attract or repel depending on the position. Yet no energy is added to this system, so how is it possible? Another example is a levitating magnet in a box. It fights against the force of gravity without any force put into the system itself.

These cases have nothing to do with Newton's first law. Newton's first law is:

The first law states that if the net force (the vector sum of all forces acting on an object) is zero, then the velocity of the object is constant.

(It's stated in many ways. That's the phrasing used on Wikipedia)

Note that the first law says absolutely nothing about energy or what forces are allowed to be on the system. All it states is that if the sum of the forces on an object is 0, its velocity doesn't change.

Ignoring Newton's first law, here's the things you were asking about in your examples:

• When you place two magnets close together and they attract/repel, the energy comes from the potential energy in the magnetic field. You put that energy into the system as part of the process of placing those magnets into place.
• Opposing a force can be done without expending energy. You will learn that the work done on an object is equal to the force applied to it times the distance it moves. In the case of a levitating magnet, it's not moving at all, so there's no work being done, meaning no energy is needed.
• It is not true that Newton's first law says nothing about energy conservation. From the first law follows that space and time are translationally invariant. From this, it follows that the energy and momentum are conserved for a closed system. Mar 24 '17 at 7:10

First of all, note that the magnetic force has infinite range. This means that at any distance, the magnets will interact with each other. Second, only total energy and total momentum of the whole system is conserved. In the case of the momentum, this is simple, because this means that magnets will attract each other and their total momentum will be zero if they were initially at rest. Energy balance is more complicated because you also have to take into account potential energy. $$E_{tot} = E_{kin} +E_{pot}$$ The gain in the kinetic energy will be compensated by the potential energy which is negative. And yes, contrary to other answers, Newton first law implies that energy and momentum are conserved. The first Law implies Galilean invariance which implies energy and momentum conservation, but of the whole system and not of its parts.

Newton's first law states that an object at rest will remain at rest, unless an external force acts upon it. In this case, there is an external force acting on it - the electromagnetic force of the magnet.

Now, how a magnet produces force is another story. I'm no expert on that particular subject, but here is a link to another stack exchange forum where it's discussed:

Why bar magnet can produce magnetic field?

Here is an article I found at Live Science on the topic:

http://www.livescience.com/38059-magnetism.html

• I think you should not answer a question by only providing a link. You should summarise what that answer says. Mar 24 '17 at 20:34
• Okay, thanks for letting me know. I read that I should show my references when providing an answer. Is it alright if I provide a link for the person to further research the topic and learn more about it? Mar 25 '17 at 3:34

Note that "work" in a physics sense doesn't mean the same as "effort" in a human sense. For example, if you hold a weight in one position in mid-air (you're a weightlifter), you would certainly think "work" is being done just holding it there, but in physics terms no work is being done in holding the weight itself in mid-air. (Although certainly there is work being done, maintaining the static position of the weight isn't "work" per se).

That's relevant to your second example, where the answer is along the lines that it's in equilibrium (balance) with gravity, not "fighting" gravity.

The system as a whole - that's the earth, the magnet, whatever the magnet is being repelled by, whatever's supporting that against gravity, and all of their related forces - is seeking the lowest overall (potential) energy level it can reach, which happens to be one where the magnet is in mid-air, so that's where it ends up and stays, until something changes.

As others have stated before, Newton's first law does not deal with conservation of energy. Also, as others have stated, no work is being done. But this doesn't mean no energy is being expended or gained.

In fact, permanent magnets aren't actually permanent. Magnetism arises from electric currents inside the magnet that exist on a molecular level. As you place one magnet close to another (or close to metal) there is an opposite electric current induced. This new opposite current subtracts from the existing current. Put simply, the magnetic current is actually being reduced over time. It will eventual go towards zero as the internal electric energy is depleted. This is why you cannot make perpetual motion machines using opposing permanent magnets.

edit: This is only the case when the magnets are moving. When they are stationary, no current is induced, no work is done, and no energy is gained or lost.