Linear magnetostatic case - wykład

Linear magnetostatic case A not entirely parallel examination of the work done, perhaps by mechanical or perhaps
by electrical means, to create a magnetic field leads to the result
Um =
1
2
μ
Z
vH·Hdv (7.4)
for the total energy stored. Of course in the case of a linear medium this result has
several alternative forms, one of which is
Um =
1
2
Z
vH· B dv. (7.5)
To see which of these results appears to be the closer to physical processes, we consider
the case where the field results from the creation in a toroidal inductor of a current by
means of a suitably variable voltage generator connected to the inductor terminals. In
any portion of the field creation process, we find the power being delivered to the circuit
is the product of the total current i (which is related to the total magnetic field H) and
the currently induced voltage v (which is related to the time rate of change of the flux
density B).
Thus in an incremental change of flux taking place over time δt, we will find the
component δUm = viδt of energy change is related to the product of H, ∂B/∂t and δt
i.e. to the product of H and δB. Thus as far as the incremental component of energy
supplied to bring about this field change is concerned, it seems that the most directly
appropriate formula is
dUm =
Z
vH· dB dv.
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