From: neufeld@helios.physics.utoronto.ca (Christopher Neufeld)
Subject: Re: Superconductors
Organization: University of Toronto Physics/Astronomy/CITA
Date: Wed, 19 Aug 1992 14:59:11 GMT

In article <pjh.714219820@nessi> pjh@eng.cam.ac.uk (Philippa Hogben) writes:
>neufeld@helios.physics.utoronto.ca (Christopher Neufeld) writes:
>>I've stored
>>electrical energy. I happen to have stored it in a magnetic field, but so
>>what? Does a rechargeable battery store electrical energy or chemical
>>energy?
>
>You have stored _energy_ in the magnetic field, not _electrical_energy_.
>"Energy may be freely converted from one form to another." [Who said that?]
>
   We're arguing semantics at this point. What is 'electrical energy'? It
isn't the kinetic energy of the electrons in the wire, it isn't really
even something you can specifically Poynt at [I know, groan].

   This all started off when I pointed out that it was misleading to say
that "electrical energy cannot be stored in a superconducting coil
because energy stored is I^2 * R and R=0, so the energy must be stored in
the magnetic field." I trust I've captured the essence of the original
statement.
   Now, strictly speaking I think that what we commonly refer to as
'eletrical energy' is that quantity whose flow is denoted by the Poynting
vector. As such there is no obvious (to me) contrivance which actually
stores Poynting vectors for later injection into a power line, so one
might argue on that count that electrical energy cannot be stored at all.
   Now, there are two ways to attack this problem, but I'll use one which
is a bit less intuitive than the quick answer in order to make a point.
The energy stored in a superconducting coil is there because it takes
energy to force currents into a configuration where the net force on the
individual current elements is such as to want to make the system expand.
The current elements have some mutual inductances which tend to oppose
the attempt to increase the current values. By pushing on it (with an
applied voltage), injecting energy into the system, you can increase
these currents. In doing so the energy in the system scales as the square
of the current, assuming that the system doesn't change its mechanical
configuration as a result of the pressures on it.
   Now, if there's a pressure, there must be a potential energy term
which has a non-zero derivative with respect to a spatial coordinate.
That term happens to be the energy density of the magnetic field, one
half of the dot product of the magnetic flux and magnetic field. In fact,
the equations which determine the inductance of the coil look
suspiciously like the equations which determine the field at all points
in space due to the coil. This is not a coincidence.
   To draw a mechanical analogy to the paraphrased sentence after the
blank line above:
   "It is impossible to store mechanical energy in water above a dam
because mechanical energy is 1/2 m * v^2 and the velocity is zero once
you've let it sit. The energy is therefore stored in the gravitational
field." I maintain that this is a somewhat artificial separation, since
you couldn't store the energy in the gravitational field without a mass,
and as such it is a misleading distinction.

>Philippa Hogben   pjh@eng.cam.ac.uk


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 Christopher Neufeld....Just a graduate student  | Confidence is the feeling
 neufeld@helios.physics.utoronto.ca    Ad astra  | you have before you
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 "Don't edit reality for the sake of simplicity" |
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