General Formulae for Energy Change - wykład

General Formulae for Energy Change In the light of the results discussed in the last two sections we will postulate that the
general expression for the change in stored energy in an electromagnetic system in response
to changes in fields is
dU =
Z
v{E · dD +H· dB}dv (7.7)
This general result is, in simple situations amenable to analysis, in accord with theoretical
results based on Maxwell's equations and the force law, and in more complex
geometries is in accord with experiments, and will thus be regarded as a correct statement
in all cases of the changes in stored energy in an electromagnetic field.
Because it is very convenient to regard the energy as actually stored within the field,
we will remove the integration and say that at any point the change in energy stored per
unit volume in a field, when the field changes, is
dW = E · dD +H· dB (7.8)
where W denotes the energy stored per unit volume of space at a point at which the
field vectors appearing in the equation above apply.
If we divide by an incremental time dt over which the energy change has taken place
and proceed to the limit, recognising the independence of both the space and time variables,
we obtain
∂W
∂t
= E ·
∂D
∂t
+H·
∂B
∂t
. (7.9)
This is the fundamental equation
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