Force on fields and definition of magnetic energy A common way of defining the magnetic work associated to the variation $\delta {\bf B}$ of the  magnetic field in a volume V, is to start with the work  done in a time $\delta t$ by the electric field, due to the presence of a time variation of B, on the current density j:
$$
\delta t \int_V {\bf E}\cdot{}{\bf j} dV.
$$
While such formula is clearly expressing the work done by the electric force due to the electric field on the currents, so it would correspond to the work done by the system described by fields on the source currents, when the formula is used as a first step to derive the work done on a system whose state is characterized by a magnetic field, at some point of the derivation  the same formula, with a change of sign, is used to represent the work done on the system containing the fields. 
The situation is reminiscent of a similar situation when one has to evaluate the work done on the system, or done by the system, in the case of a gas in a container with a moving wall. However, in that case, the "object" on which work is done is always the moving wall. What changes is the force due to the internal or to the external system. In absence of friction and for a quasi-static transformation they are equal and the work evaluated in the two ways are exactly opposite.
In the magnetic field case, it seems to me that in order to justify using $-\delta t \int_V {\bf E}\cdot{}{\bf j} dV$ as the work done on the system characterized by the magnetic field, some extension of the concept of work would be required. Is there anything like the concept of "work on a field"? References ?
Note added some time after posting:
The expression "work on a field" (including the quotation marks) is explicitly used in Landau&Lifshitz Electrodynamics of continuous media.
I add that using conservation of energy to avoid the difficulty seems to me conceptually wrong, since the whole derivation of magnetic work is supposed to be done in order to show that it is possible to define operationally a magnetic energy. For such a reason I do not think that  the answers to a related question ( Work producing current = energy stored in the magnetic field? ) really have addressed this last conceptual point.
 A: After additional time, I have got some idea about a possible way to clarify the issue about the work done on the field. Hoping that it might be a starting point for even better answers, I'll try to collect here my present understanding.
Basically I have reconsidered the approach by Panofsky and Phillips Classical Electricity and Magnetism: Second Edition. In section 10-1 they start with the time rate a bactery with an electromotive field ${\bf E^{\prime}}$ does work on the current distribution generating the magnetic field. The current $\bf j = \sigma (E^{\prime}+E)$, present in conductors of conductivity $\sigma$, is due to the total electric field ${\bf E^{\prime} + E}$, where ${\bf E}$ is the electric field due to the magnetic induction (Faraday law) present during the whole transient time. The energy transfer rate from the bactery to the currents and finally to the magnetic field is clearly
$$
{\bf j \cdot E^{\prime}}= \frac{j^2}{\sigma} - {\bf j \cdot E}
$$
where the first term in the right hand side of the equation accounts for the power going into Joule heating.
Therefore, $-{\bf j \cdot E}$ is clearly the electric power (energy rate) going into the induced magnetic field.
I think that the key point I was missing is to clearly distinguish between the applied external field $\bf E^{\prime}$ and the induced electric field  $\bf E$
