What is the origin of electrical potential energy in a charged particle's field?

[AlexPick]

I'm currently a Junior in high school and am quite interested in becoming a particle physicist. I have used this site many times before to answer questions, but only when already asked by others. In this case, I finally made an account since I cannot find a good explanation anywhere so here's to hoping my first post gets answered!

In reading my physics textbook and teaching myself the basics of electromagnetism I have familiarized myself with the concept of an Electric Field and Electric potential energy and have a question relating to the PE. Consider a hypothetical system consisting of only a stationary positive electric charge, a metal coil, and a bar magnet. If the bar magnet is moved into the coil, a time-varying magnetic field is generated and according to Faraday's law of induction a corresponding electric field. I understand that when the magnet is not moving there is no induced EMF, so I just want to consider the initial creation of the electric field and the properties of the system while it exists. Electric potential energy I have learned is stored in the electric field of a charged particle and at the moment the electric field is generated, the charged particle in the field should acquire a certain potential energy. My question is:
What form of energy is converted into the electrical potential energy stored in the charged particle's field and from what part of the system does this energy originate?
Thanks in advance,
Alex

 

[zush]

The thing is, it takes energy to oscillate the magnet which passes through the metal coil. This is the energy which becomes the work done by the electric field.

 

[AlexPick]

I figured it would probably end up being the energy put into moving the magnet that generates the magnetic field but I would like more specifics please. When the magnet is moved, what happens? Is the magnetic potential energy stored in the magnetic field transformed into electrical potential energy when it varies? If so, I'm still not sure I understand how the electrical potential energy stored in the field around the conducting coil becomes the potential energy stored in the particle's field. Correct me if I am incorrect, but the electric field in any given area is just the sum of the individual electric fields due to charged particles or varying magnetic fields, right? If this is true, then that may resolve my question. Would the electrical potential energy be stored in the combined field produced by the magnet and particle?

 

[zush]

I figured it would probably end up being the energy put into moving the magnet that generates the magnetic field but I would like more specifics please. When the magnet is moved, what happens? Is the magnetic potential energy stored in the magnetic field transformed into electrical potential energy when it varies?

For true specifics, you're going to have to take some four years of college and then graduate school to learn about quantum electrodynamics, or QED. There's a great book on it by Richard Feynman.

 

[AlexPick]

Feynman is my favorite physicist! :D Ya, I have been reading Griffiths Introduction to Elementary Particles, and though conceptually I can understand about 80% of the stuff, the mathematics is way over my Calculus-I knowledge. I've been having a lot of trouble finding a comprehensive list of mathematical areas of study required to properly understand quantum mechanics and particle physics. Do you have any suggestions?

 

[Drakkith]

I figured it would probably end up being the energy put into moving the magnet that generates the magnetic field but I would like more specifics please. When the magnet is moved, what happens? Is the magnetic potential energy stored in the magnetic field transformed into electrical potential energy when it varies? If so, I'm still not sure I understand how the electrical potential energy stored in the field around the conducting coil becomes the potential energy stored in the particle's field. Correct me if I am incorrect, but the electric field in any given area is just the sum of the individual electric fields due to charged particles or varying magnetic fields, right? If this is true, then that may resolve my question. Would the electrical potential energy be stored in the combined field produced by the magnet and particle?

The magnetic field produced by the magnet pushes and pulls charges in certain directions. When the magnet isn't moving the charges "balance" themselves out with the static field and are stationary. When you move the magnet you now have a moving magnetic field. Since this field is penetrating the conductor and varies in strength depending on distance, moving the field puts more pressure on some particles than others, which results in current flow.

At the start of the system, when everything is stationary, there is no potential energy as there is no other force other than the single charge. (Lets assume that the magnet is far enough away as to exert effectively no force on the particle) When you move the magnet it generates an electric field in the conductor. Once this field is generated you now have another source of charge in the system. How much "potential energy" is there will depend on the strength of the charge in the conductor and the distance between it and the particle. A higher difference in charge strength will result in more potential energy.

I think you're confused by the term "potential energy". Energy isn't a "physical" substance. It isn't a THING at all. Here's the definition of energy from wikipedia:

In physics, energy (Ancient Greek: ἐνέργεια energeia "activity, operation"[1]) is a quantity that is often understood as the ability a physical system has to do work on other physical systems.[2][3] Since work is defined as a force acting through a distance (a length of space), energy is always equivalent to the ability to exert pulls or pushes against the basic forces of nature, along a path of a certain length.

Imagine we have a single particle in the universe. Nothing else. There is ZERO energy of any kind here. Why? Because there isn't any other system to act upon! No other particles, no nothing. Now, let's look at two particles in this universe at X distance from each other. They both will act upon each other, causing their positions and speed to change somehow. This ability for something to cause a change in something else is what we call energy.

 

[Dadface]

The energy changes are described by Lenz's law.When the magnet (or coil) move the induced current causes the coil to become magnetised and in a direction such that it opposes the change producing it.When the magnet and coil are pushed closer together they repel and when they are pulled further apart they attract.It is the energy input needed to overcome these forces of repulsion/attraction that is converted to electrical energy.

 

[BruceW]

About the op's question on where the energy in the electric field comes from:
First imagine there are no charges. If the magnet was not moving, there is no electric field, so all the energy is stored in the magnetic field:
$$energy \ density = \frac{B^2}{2 \mu}$$
Then imagine the magnet was given K.E. by someone, the work done by the person equals the K.E. received by the magnet. Also, the magnetic field is now time-varying, since the magnet is moving, so an electric field will be created. So now some of the energy is stored in the magnetic field and some in the electric field.
$$energy \ density = \frac{E^2}{2 \varepsilon } + \frac{B^2}{2 \mu}$$
Energy is conserved, and since the K.E. was supplied by the person, it means the total energy density (integrated over all space) must be the same as before. Therefore, the energy stored in the magnetic field becomes less, since some of the energy is now stored in the electric field.

In conclusion, a moving magnet has a slightly less strong magnetic field, to provide the energy to create the electric field. If you notice in the equation for energy density, the energy density due to the magnetic field is absolutely huge compared to the energy density due to an electric field of similar magnitude. (Because of the relative values of epsilon and mu). Therefore, the magnetic field is only reduced slightly to create a fairly large electric field.

So that's how the magnet makes the electric field. Now, if we think about the coil, the charges in the coil will be pushed round due to the electric field created by the magnet. Therefore, the moving charges create their own magnetic field which opposes the change in magnetic flux through the coil. Therefore, when the magnet is moving toward the coil, the magnetic field from the charges is opposite to the magnetic field from the magnet, and the magnet is slowed down. And when the magnet comes out of the coil, the magnetic field due to the charges is in the same direction as the magnetic field of the magnet, so the magnet is sped up on the way out.

 

[BruceW]

Sorry, the magnet is slowed down on the way out

 

[AlexPick]

Drakkith: I understand that energy isn't a tangible thing, but that wikipedia definition is kind of simplistic. It is the definition that is most convenient when discussing it, but even incredibly well learned physicists have trouble explaining it. As for the hypothetical system you discussed, I assume you are only talking about electric potential energy, because if not then you are incorrect. The particle would still have energy by virtue of its mass (or rather, the other way around. The fact that the particle exists at all indicates that there is energy in the system.). While energy itself is not tangible, it still has a physical nature do to it's expression as mass... Even the electric field has mass do to its storage of energy, so to say that energy isn't "physical" is only half true. "Because there isn't any other system to act upon! " There being no system to act upon does not preclude the ABILITY to do work, so even by the definition you quoted you would still be incorrect. A one particle universe would still have energy.
Everyone: Thanks a lot for your responses! I didn't really get a straight answer as to whether what I said was correct, but Bruce's explanation seems to confirm that it was.