How is energy stored in a field?

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In these 3 fields:

1. An electric field

2. Magnetic field

3. Gravitational field

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I only learned the mathematical formulation of energy. The intimate nature of each field and the way of storing energy are issues never addressed by my teachers. I never spent time looking for the subject in scientific publications. And the answer has not come to me casually.

Within classical physics, they are very interesting questions. I will follow this thread because I would like to read some didactic response.

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@ Hulk

You seem to be annoying someone here, judging from your increasing collection of red points.

I don't normally give these but this is the last time I will answer a question of yours if you don't engage in discussion about the subject.

This list looks very similar to the one I gave last time you asked this question.

The short answer is that in all cases the energy is due to the interaction of two bodies endowed with the property of interest.

It is measured as work done positioning these bodies relative to each other.

In more technical words two sources.

In the case of magnetic fields one body may also self interact since a single source magnetic (magnetic monopole) has never been seen.

The field itself is a mathematical construct, not some magic fluid you 'pump up' with energy.

Edited by studiot

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You don't need two bodies to have energy stored in a field. If a star emitted light a billion years ago and you telescope catches it now, the comfortable law of energy conservation wants energy to have been stored in the vacuum in the meantime.

An extreme case is when an electron-positron pair annihilates. At the time you catch a gamma ray, both particles don't exist any more.

How is that energy stored? I ignore it. I don't even know what energy is.

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14 hours ago, Enthalpy said:

You don't need two bodies to have energy stored in a field.

An extreme case is when an electron-positron pair annihilates

Since you have asserted the direct opposite of my comment I feel I should reply.

What exactly are an elecrton and a positron if not two bodies?

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15 hours ago, Enthalpy said:

You don't need two bodies to have energy stored in a field. If a star emitted light a billion years ago and you telescope catches it now, the comfortable law of energy conservation wants energy to have been stored in the vacuum in the meantime.

The energy is in the photons. No field is necessary.

15 hours ago, Enthalpy said:

An extreme case is when an electron-positron pair annihilates. At the time you catch a gamma ray, both particles don't exist any more.

Where is the field?

15 hours ago, Enthalpy said:

How is that energy stored?

They aren't examples of energy being stored in a (classical) field?

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After the positron-electron pair annihilates, we still want the energy to be present before it's absorbed by an other particle, for instance at a detector. Some effects of this energy, like its gravitational attraction on massive bodies, are perceivable before the photons are destroyed.

Energy carried by the photons: if you wish. But it's not a reason to dismiss the field.

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Why do you need 2 bodies to store energy in a field? Doesn't every body contain energy? (E=mc²)

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4 minutes ago, Itoero said:

Why do you need 2 bodies to store energy in a field? Doesn't every body contain energy? (E=mc²)

Yes indeed, but a massive (= a body with mass) is not a field.

And the question was

Quote

How is energy stored in a field?

The field is needed because (classically) it is the medium of interaction between two or more bodies.

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3 hours ago, Enthalpy said:

After the positron-electron pair annihilates, we still want the energy to be present before it's absorbed by an other particle, for instance at a detector. Some effects of this energy, like its gravitational attraction on massive bodies, are perceivable before the photons are destroyed.

Energy carried by the photons: if you wish. But it's not a reason to dismiss the field.

48 minutes ago, Itoero said:

Why do you need 2 bodies to store energy in a field? Doesn't every body contain energy? (E=mc²)

What field are you referring to?

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E and H. Or psi if you prefer, suits few particles better.

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The 'energy of a field' ( not an accurate description ) is essentially the configuration of the system.
It is clearly seen in the case of potential energy; being described as the position of a test object with respect to the potential field.

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1 minute ago, MigL said:

The 'energy of a field' ( not an accurate description ) is essentially the configuration of the system.
It is clearly seen in the case of potential energy; being described as the position of a test object with respect to the potential field.

Thank you MigL +1

So you have the test object and the source of the field.

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I don't deny the validity of field-models. But you imo just need one body to have (measurable) energy...regardless of the field you are in.

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10 minutes ago, Itoero said:

I don't deny the validity of field-models. But you imo just need one body to have (measurable) energy...regardless of the field you are in.

It's not a matter of opinion it is a matter of definition.

Gravity is the simplest classical field so with reference to that one, consider a single particle with mass.

Now state please what it's gravitational energy is without reference to a test particle.

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7 minutes ago, studiot said:

consider a single particle with mass

E=mc²

9 minutes ago, studiot said:

Now state please what it's gravitational energy is without reference to a test particle.

? That's wat I said....you need one particle/body.

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So you are claiming that the gravitational energy of a body is given by Einstein's relation E = mc2 ?

Gosh that is quite a difference from the classical value.

Edited by studiot

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When you place a body with mass in a gravit field then you have stored energy.

7 minutes ago, studiot said:

So you are claiming that the gravitational energy of a body is given by Einstein's relation E = mc2 ?

No but the OP doesn't ask for gravitational energy. He asks how you store energy.

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13 minutes ago, Itoero said:

When you place a body with mass in a gravit field then you have stored energy.

Yes of course, but

Where does the gravitational field come from?

14 minutes ago, Itoero said:

No but the OP doesn't ask for gravitational energy. He asks how you store energy.

I hope you are not being facetious.

2 hours ago, studiot said:

So you have the test object and the source of the field.

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13 minutes ago, studiot said:

Where does the gravitational field come from?

What does that matter?

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Are you saying you can store energy in a gravitational field without a gravitational field?

What is the only known classical source of a gravitational field?

1 minute ago, Itoero said:

What does that matter?

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1 minute ago, studiot said:

Are you saying you can store energy in a gravitational field without a gravitational field?

No.

3 minutes ago, studiot said:

What is the only known classical source of a gravitational field?

a massive body

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5 minutes ago, Itoero said:

a massive body

So you have two bodies.

The massive body and the body you place in its field.

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44 minutes ago, studiot said:

So you have two bodies.

The massive body and the body you place in its field.

Yes, In that sense, you have two bodies.

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4 hours ago, Itoero said:

Yes, In that sense, you have two bodies.

Thank you.

I hope you now understand that this idea can be extended to all classical fields although some are a bit more complicated than others, the magnetic field is proobably the most complicated.

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