[syhprum (OP)]

If I take a one cubic meter of space where in a magnetic field of 1 Telsa exists how much energy does that represent ?.
I have always believed that the large amount of energy stored in atomic Hydrogen that is liberated when it forms into the molecular form is due to the magnetic field generated by its single Electron, is this view correct ?.

[syhprum (OP)]

I have been reading what 'Wiki' and other sources have to say on the matter and am not surprised by the lack of comments.

[lyner]

If I take a one cubic meter of space where in a magnetic field of 1 Telsa exists how much energy does that represent ?.
I have always believed that the large amount of energy stored in atomic Hydrogen that is liberated when it forms into the molecular form is due to the magnetic field generated by its single Electron, is this view correct ?.

I'm not sure there is an answer to that one. Field is the gradient of potential and more information would be needed. Your question is, I think, analogous to asking what energy corresponds to a measured 'g' on the surface of a planet. The work required to lift a kg mass off the surface and take it to infinity (the definition of Potential) would depend upon the values of mass and density of the planet. So I think there is a similar situation here. You would need to know 'something else'. I can't think what but it must relate to how the field has been set up - for instance the number of turns, the area and the current in the coil producing the field.

[syhprum (OP)]

let us assume we have a solenoid of length one meter and an area of one meter wound with one thousand turns of zero resistance conductor passing a current sufficient to generate a magnetic field of 1 Telsa.
This solenoid is parallelled by a resistor of 1 Ohm, when the supply of current is interrupted the energy stored in the magnetic field is dissipated in the resistor, how much ?

Using an old formula from wireless consruction in the twenties for the inductance I make it 1 Henry but do not know how to calculate the current required to produce this field strength.

[syhprum (OP)]

It is of course possible to calculate how much energy the gravitational field of a body represents (which is negative!), one often sees the formula written on the blackboard in pseudo scientific adverts.

[lyner]

The potential is given by the integral of the field from infinite to the point of interest. That means to have to know more than just the field. You could, for instance, be on the surface of a dense planet or on the surface of a gas giant and measure the same field. The potential in both cases would be different.

I will look into the answer to your magnetic question. I believe you have given enough details, now. I will retire with an ice pack round my head.

[lyner]

The field in the centre of a solenoid is given by
B = μ₀I N/L
ref http://plasma.kulgun.net/sol_page/
(independent of the area, I notice)

for N turns, length L and current I
μ₀ = 4π E^-7
This seems to suggest that a current of about 800A is needed to give you 1T of field.

The energy in an inductor is given by I²L/2

Using your 1H value for L, this looks like 0.32MJ.
The energy depends upon the field AND the area of the coils.

My arithmetic is always suspect so the numerical answer could always be wrong but the principle is ok.

[syhprum (OP)]

I recall reading somewhere that a 40T field contains as much energy as the equivalent volume of TNT explosive, your enlightening calculation seem to bear this out.
High intensity superconducting magnets such as used in the LHC have been known to go off with an awful big bang!

[lyner]

Yes. The forces involved are very high when the permability is increased. Even a humble, small, mains transformer will rattle violently under load if it's not clamped and stuck together.

[Bored chemist]

I have always believed that the large amount of energy stored in atomic Hydrogen that is liberated when it forms into the molecular form is due to the magnetic field generated by its single Electron, is this view correct ?.

I doubt it.
The energy stored in a piece of magnetised steel can be released by heating it to the curie temperature; it's not a lot of energy.
The energy released by the combination of two atoms of hydrogen is very large and arises from the electrostatic atraction of the electron of each atom and the nucleus of the other.
Whether the two electrons are magnetically alligned or not gives rise to the difference between ortho- and para- hydrogen. The effects of that difference are usually only apparent at very low temperatures because the energy difference involved is so small.

[lyner]

If the magnetic energy is governed by the area of the loop and the current is small, would you expect a lot of energy? On the other hand, the electric potential would be inversely proportional to the separation. . . . . .  The electric would take over from the magnetic as you decrease the dimensions of the system.

[lightarrow]

If I take a one cubic meter of space where in a magnetic field of 1 Telsa exists how much energy does that represent ?

In the void, the magnetic field energy density is:

u = (1/2μ₀)|B|²

For |B| = 1T, since μ₀ = 4π•10^-7H/m, you have:

u = 1/8π•10^-7 = 3.979•10⁵ J/m³

which, for a volume of 1m³ means (if B is uniform):

E = 1*3.979•10⁵ = 3.979•10⁵ J ~ 400,000 J.

[syhprum (OP)]

It is interesting to receive two answers one from an engineering point and one from a more theoretical point of view.
They vary by a factor of 20% or so which seems quite reasonable for the two approaches it may well be that my formula for the inductance is not quite correct

L (μH) =.2A^2*N^2/3A+9B    A=dia, B=Length N=No of turns (all in inches!)

[lyner]

Interesting but no surprise, when you think of the care that went into the original work. (not mine!)