# Homework Help: Force Fields

1. Jan 12, 2004

### eddo

This question is more regarding terminology than anything. It's from one of my assignments. The question is can you store energy in and release energy from a force field? I don't really understand what is being asked. I know you can store potential energy in objects in the force field, and technically mass is energy and that can be stored and released. Any and all help will be greatly appreciated. Thank you.

2. Jan 12, 2004

### gnome

Energy is stored in the electric field of a capacitor and in the magnetic field of an inductor.

I suppose we can also say that energy is stored in a gravitational field. For some reason I'm much more hesitant about that one. It sounds odd; but when you think about it, no more odd than having energy stored in the electromagnetic fields. (Or maybe gravitational potential energy is stored in the object that is in the field? I'll be interested to see what others have to say about this.)

3. Jan 13, 2004

### Arcon

I really hate it when people try think of energy as being stored since it makes one think that the energy has a location.

I think what the assignment is refering to is that in the equations you will see field quantities. For example: Consider a charged particle in an inertial frame of referance, S. In S let there be an EM field which has a constant magnetic field (i.e. does not depend on time but may vary with position). Then the electric field is given by

$$E = -\nabla \Phi$$

where $$\Phi$$ is the Coulomb potential (aka electric potential). The electric potential energy, V, is defined as

$$V = q\Phi$$

Suppose you place a particle in such a field. Now do work on the charge to move in from one position to another. The potential energy will have changed. If you did work on it then energy left you and has to show up somewhere else. That energy shows up in the increase in the potential energy. I guess you can say that now the field has energy stored in it. But that's not a very meaningful thing so say since the total value of energy can always be set equal to zero with no change in the physics. Only changes in energy make sense.

Arcon