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Hi Folks --
Every time I see the term "conservative force" I wince. That's
because there seems to be a very high likelihood that whatever
is being said about the "conservative force" is wrong.
For present purposes (and a lot of other purposes besides)
I recommend saying
/grady/ instead of conservative, and
/non-grady/ instead of non-conservative.
A non-grady force is not the gradient of any potential. Some
techniques for visualizing non-grady fields are presented here:
http://www.av8n.com/physics/non-grady.htm
The grady/non-grady concept applies just fine to things other
than forces. An important example is the electric field, which
may or may not be the gradient of some electric potential.
Another example is thermodynamic work, which (except in trivial
cases) is not the gradient of any thermodynamic potential, i.e.
not the gradient of any function of state.
The poster child for a non-grady field is the electric field
in a betatron. If you want to express this as a force, stick
in a test charge and talk about the force on the test charge.
===============
It is very common to find people talking about conservative
and non-conservative forces in the same breath as conservation
of energy. This is a huge mistake! Please don't do that. I
recommend not using the terms conservative and non-conservative
at all, and using grady and non-grady instead ... especially in
the context of conservation of energy.
Energy is always conserved. Strictly conserved. Locally conserved.
The existence of non-grady forces does not change this, not even
a little bit. Energy is conserved. Period. Energy is conserved!
Exclamation point!
The only way you could fool yourself into thinking that
non-grady forces are exceptional is if you focus undue
attention on some subset of the energy, perhaps by excluding
the field-energy in the betatron. This is a red herring, i.e.
an unhelpful distraction, because we never expected some
random subset of the energy to be separately conserved.
This problem seems to be particularly prevalent in high-school
materials. College-level stuff tends to mention "non-conservative"
forces only very briefly, if at all.
===
Secondly, even if we accept that non-grady forces conserve energy,
it would be quite wrong to associate non-grady forces with friction,
dissipation, and irreversibility.
Example: The motion of an electron in a betatron field is entirely
reversible and non-dissipative.
Frictional forces tend to be both non-grady and dissipative, but
this is only an example, and is not representative of non-grady
forces in general.
======================
To summarize:
*) Non-grady fields exist, and indeed are quite common.
-- Do not assume that every force is the gradient of some potential.
-- Do not use the term "electric potential" as a synonym for voltage,
because most voltages are not potentials; they are path-dependent.
*) Do not use terms like "conservative" or "non-conservative" force
at all. Such terms are begging to be misunderstood. Students
are going to associate such terms with conservation of energy,
which is just utterly wrong.
*) Do not assume that a non-grady force is dissipative or irreversible.
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