# Does a magnetic field have mass?

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Can energy exist on it own ? The answer is no it can't.  It is a property defined as the ability to perform work. You can't have momentum without having something that moves can you ?

When you put particles in a box those particles can exert pressure on the container walls.

Answer this question  how can a laser propel a solar sail if light cannot gain mass through the relation I posted ?

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6 hours ago, MPMin said:

Perhaps this is also point in contention in its own right, is the magnetic field around a wire actually static or is it emanating? My guess is that it’s constantly emanating outward from the wire.

If the current is static, then the field is static.

6 hours ago, MPMin said:

I don’t understand how there can be momentum without mass when p=mv?

That equation for momentum is only for objects with mass (where, therefore, v < c).

6 hours ago, MPMin said:

I’d ask you to please show me how momentum is conserved in a system that loses E out of the system?

Momentum is always conserved in a closed system. But if energy or mass is leaving the system , it is not closed.

6 hours ago, MPMin said:

What I mean is mass is easily accounted for because doesn’t easily convert to energy but energy easily converts to other forms of energy which is why most energy systems are not 100% efficient

Mass is easily converted to energy. We do it all the time when we burn fuel to power a car, for example.

If you were to burn a candle in a sealed container but let the heat escape, then the container would have less mass afterwards.

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8 hours ago, MPMin said:

Perhaps this is also point in contention in its own right, is the magnetic field around a wire actually static or is it emanating? My guess is that it’s constantly emanating outward from the wire.

A DC field is static. It can't be constantly emanating, because you can't reach a steady state without a sink of some sort.

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I don’t understand how there can be momentum without mass when p=mv?  if you’re going to say p=E/c as well I’d ask you to please show me how momentum is conserved in a system that loses E out of the system?

If you have identical energetic particles ejected in opposite directions, momentum would not change, and energy would be reduced.

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What I mean is mass is easily accounted for because doesn’t easily convert to energy but energy easily converts to other forms of energy which is why most energy systems are not 100% efficient

No, mass is energy. Saying anything along the lines of "mass is converted to energy" is wrong, or at least a sloppy way of expressing the concept (and physicists do get into bad habits when discussing these things, because we know what the person means). Mass converts to other forms of energy.

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2 hours ago, Strange said:

If the current is static, then the field is static.

I think you mean if a current is constant then the field is constant, I don’t think there is such a thing as a static current.

24 minutes ago, swansont said:

A DC field is static. It can't be constantly emanating, because you can't reach a steady state without a sink of some sort.

I disagree that any magnetic field created by a current is ever static. An emp can be created by pulsing a direct current, also consider the instant moment a direct current begins, does the magnetic field immediately propagate the area it will eventually occupy or does the magnetic field have to emanate from the wire to propagate the area?

3 hours ago, Strange said:

If you were to burn a candle in a sealed container but let the heat escape, then the container would have less mass afterwards.

Let’s say you burn the candle in the container and the container gets hotter  from the candle burning (I know I should be saying the container gains thermal energy but I don’t want to because you know what I mean), does this mean the mass of the container was increased while the container was hotter?

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50 minutes ago, MPMin said:

I think you mean if a current is constant then the field is constant, I don’t think there is such a thing as a static current.

Yes the correct term for a current that does not change with time is a steady current.

A constant current is a horse of a different colour entirely.

Currents are concentrated phenomena, fields are distributed phenomena.

Magnetic effects are brought about by time variation.

Either the current is time varying in which case the field varies in sympathy.

or the field is non uniform, although steady.

In which case the time element is brought about by motion from one part of the field to a different part where the field is different.

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49 minutes ago, MPMin said:
I disagree that any magnetic field created by a current is ever static. An emp can be created by pulsing a direct current, also consider the instant moment a direct current begins, does the magnetic field immediately propagate the area it will eventually occupy or does the magnetic field have to emanate from the wire to propagate the area?

I specified a DC field. I didn't say any field, and I had commented earlier that I was discussing DC/static fields, as this is what the OP implied. Bringing up EMPs (again) is taking my discussion out of context.

49 minutes ago, MPMin said:

Let’s say you burn the candle in the container and the container gets hotter  from the candle burning (I know I should be saying the container gains thermal energy but I don’t want to because you know what I mean), does this mean the mass of the container was increased while the container was hotter?

Yes, warmer objects have more mass than cooler ones. E = mc^2 The full equation is E^2 = p^2c^2 + m^2c^4, which reduces to E = mc^2 when an object is at rest (i.e. no CoM KE)

Thus, energy that is not due to CoM motion is proportional to the mass, and vice versa. Hot vs cold, or spinning vs not spinning. The former has more energy than the latter, all else being equal.

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58 minutes ago, MPMin said:

I disagree that any magnetic field created by a current is ever static.

Again the term is steady not static.

'Static' magnetic fields have a special meaning relating to machinery, to distinguish between moving parts.

All magnetic fields are generated by moving charges, even those in permanent magnets which have steady fields.

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24 minutes ago, studiot said:

Magnetic effects are brought about by time variation.

Either the current is time varying in which case the field varies in sympathy.

or the field is non uniform, although steady.

In which case the time element is brought about by motion from one part of the field to a different part where the field is different.

No, I disagree. The Magnetic field of a current-carrying wire is proportional to the current. If the current is constant, the field will not be changing in time. i.e. there is no time variation. If there is, there will also be an electric field present (the dB/dt term in the time-dependent Maxwell's equations. But there are time independent versions of the equations, and give rise to static fields)

The non-uniformity of the field is spatial, not temporal (I'm ignoring the transient when the field is turned on)

Also, the electron's magnetic field (and that of other quantum particles) is not due to motion, though it is a QM analogue of motion (intrinsic angular momentum) But in the case under discussion, yes, the current is electron motion.

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Judging from the question regarding the candle it occured to me that we should clarify a detail.

Mass doesn't mean weight. Mass is the resistance to inertia change. Just wanted to add this point just in case as that is a common misconception.

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2 hours ago, MPMin said:

I think you mean if a current is constant then the field is constant, I don’t think there is such a thing as a static current.

I think I meant  if the current is constant then the field is static.

2 hours ago, MPMin said:

Let’s say you burn the candle in the container and the container gets hotter  from the candle burning (I know I should be saying the container gains thermal energy but I don’t want to because you know what I mean), does this mean the mass of the container was increased while the container was hotter?

No, because the heat energy in the container (ignoring radiation/conduction losses for the moment) comes from the mass lost in burning.

Then the heat will radiate away and the container will have less mass.

48 minutes ago, Mordred said:

Mass doesn't mean weight.

Good point. (I did originally write "weigh less" as a more familiar concept in my "candle" example. Then realised it could cause more confusion!)

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1 hour ago, swansont said:

(A) No, I disagree. The Magnetic field of a current-carrying wire is proportional to the current. If the current is constant, the field will not be changing in time. i.e. there is no time variation. If there is, there will also be an electric field present (the dB/dt term in the time-dependent Maxwell's equations. But there are time independent versions of the equations, and give rise to static fields)

(B) The non-uniformity of the field is spatial, not temporal (I'm ignoring the transient when the field is turned on)

(C) Also, the electron's magnetic field (and that of other quantum particles) is not due to motion, though it is a QM analogue of motion (intrinsic angular momentum) But in the case under discussion, yes, the current is electron motion.

(A) Sorry by my points stand.

Yes the mag field is proportional to the current so what? I did not say otherwise.
But constant current means only that the current doe not change regardless of the voltage.
You can have a constant current that changes with time. You can even buy CC power supplies to achieve this. That is how LED dimmers work.
I am sure that the correct term is steady current for a current that does not change with time.

(B) That is what I said

(c) There are classical models that consider the field of a permanent magnet as due to charge carrier motion. I agree there are also more refined modern ones.

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6 minutes ago, studiot said:

You can have a constant current that changes with time.

Not in my dialect of English. (Unless this explicitly specified, "the current is a constant 2 A for the first hour and then drops to a constant 1A")

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But constant current means only that the current doe not change regardless of the voltage.

That is one use of the term. Not the only one.

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4 minutes ago, studiot said:

(A) Sorry by my points stand.

Yes the mag field is proportional to the current so what? I did not say otherwise.
But constant current means only that the current doe not change regardless of the voltage.
You can have a constant current that changes with time. You can even buy CC power supplies to achieve this. That is how LED dimmers work.
I am sure that the correct term is steady current for a current that does not change with time.

You said "Magnetic effects are brought about by time variation." Where is the time variation with a DC current, (which, be definition, does not vary in time)?

If the current changes, it is not constant. Constant implies it has the same value.

4 minutes ago, studiot said:

(B) That is what I said

You said "Magnetic effects are brought about by time variation."

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45 minutes ago, swansont said:

Where is the time variation with a DC current, (which, be definition, does not vary in time)?

46 minutes ago, Strange said:

Not in my dialect of English. (Unless this explicitly specified, "the current is a constant 2 A for the first hour and then drops to a constant 1A")

This variation of terminology is probably part of the reason why so many pupils are turned off Physics at school.

Different teachers telling them conflicting things tends to do that.

How would you describe the output of a half wave rectifier, with no filter?

Would you call it DC ?

Would you say it is time varying?

Would you say it is constant?

Would you say it is steady?

How would you describe the observation that every complete cycle the measurement would be the same. Would you call this constant?

53 minutes ago, swansont said:
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(B) That is what I said

You said "Magnetic effects are brought about by time variation."

Yes this shows that I, too , should be more careful with terminology.

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1 hour ago, studiot said:

This variation of terminology is probably part of the reason why so many pupils are turned off Physics at school.

The fact that words can have more than one meaning, and that can be context dependent, is not unique to physics.

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1 minute ago, Strange said:

The fact that words can have more than one meaning, and that can be context dependent, is not unique to physics.

So would you say that you can have a constant alternating current?

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Just now, studiot said:

So would you say that you can have a constant alternating current?

Yes and no.

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Well not constant when you consider flow of charge under vectors.

However an average current could be considered constant

Edited by Mordred

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1 hour ago, Mordred said:

However an average current could be considered constant

Consider the filter capacitor of a DC power supply where the load is fixed and drawing a steady current that therefore has a constant value.

The current into said capacitor spikes very like the EMP that was being argued about earlier, yet, on average it produces a steady constant value.

Would you call the input 'constant' ?

7 hours ago, swansont said:

The non-uniformity of the field is spatial, not temporal (I'm ignoring the transient when the field is turned on)

5 hours ago, swansont said:
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(B) That is what I said

You said "Magnetic effects are brought about by time variation."

I did, but you also quoted all that I said wherein I detailed several ways in which the  field might vary one was indeed in time, the other was in space.

So that is what I said.

Though I agree the wording could have been better.

Thank you to whoever liked my original input. I rather felt the OP was receiving a pedantic hard time with some rather questionable definitions.

I was trying to make it as easy for him as I could.

I am sorry if I over simplified but as can now be seen the isuue of 'constant' is not clear cut.

Edited by studiot

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19 hours ago, MPMin said:

I don’t understand how there can be momentum without mass when p=mv?

I think other members have responded in detail, I probably should have written that the photons in the EMP has zero invariant* mass. I find it interesting that there was an earlier concept of a specific "electromagnetic mass". Modern physics instead use mass–energy equivalence instead of electromagnetic mass, but it still can be found** in older material.

Regarding steady vs constant***. For what it is worth Feynman says: "magnetic fields associated with steady currents—the subject of magnetostatics". I had to check since in my first language the meaning of steady, constant and related words sometimes kind of overlap with "reliable" current (free from unwanted fluctuations).

*) or "rest" mass
**) For instance  "Electromagnetic mass", The Feynman Lectures on Physics, 2 http://www.feynmanlectures.caltech.edu/II_28.html

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With regards to the OP...

A vector field such as the electromagnetic field ( or electric and magnetic fields ) has an associated energy density, the measure of energy stored in the field per unit volume of space.
As such, it is the measure of a property of that volume of space.
But it could also be interpreted as a measure of a property of the field.

So if the field can be said to possess the property of energy, it must, by definition, also possess the property of mass.

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18 hours ago, Strange said:

Mass is easily converted to energy. We do it all the time when we burn fuel to power a car, for example.

Does this apply to chemical reactions that balance? The mass of one side of the equation always equals the other side thus no loss of mass occurs according to chemical equations.

12 hours ago, Strange said:
13 hours ago, Mordred said:

Mass doesn't mean weight.

Good point. (I did originally write "weigh less" as a more familiar concept in my "candle" example. Then realised it could cause more confusion!)

What’s wrong with quantifying mass by weighing it?

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Place that same weighed object and weigh it on the moon. The weight will be different but the mass would be the same.

Edit I should be more precise here  the invariant mass would be the same. Under GR graviton all mass is identical to inertial mass.

$m_g=m_i$ the subscript i  denotes  inertial mass (relativistic mass or variant mass ) with last being modern usage. rest mass and relativistic mass caused too much confusion. Those terms are replaced with invariant and variant respectively. (Also works better with tensors in gauge group theories such as relativity)

Edited by Mordred

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33 minutes ago, Mordred said:

Place that same weighed object and weigh it on the moon. The weight will be different but the mass would be the same.

Edit I should be more precise here  the invariant mass would be the same. Under GR graviton all mass is identical to inertial mass.

$m_g=m_i$

But practically speaking what’s wrong with quantifying mass by weighing it on earth?

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Different locations on Earth can have different gravitational potentials even at sea level. Same problem.

Next definition of importance.

Potential energy is the energy due to field location. (Applies to all field treatments)

Obviously kinetic energy is due to the objects motion.

(This stress tensors employ thus through the full Einstein field equatioms) so does QFT (QED etc)

Side note test of GR. They have measured time dilation at 1/2 foot difference.

Edited by Mordred

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