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I don't understand what does magnetic field energy density stand for? The possible work that the magnetic field can do? So we can calculate the amount of "work" it can do just from the energy density?

Example: A magnetic field is created by a solenoid, there is a energy density of 10J/m3. From that can I derive the magnitude of magnetic force using work = F*d Thus, it would be F = W/d?

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This is a measure of the energy stored in an inductor. Energy density only makes sense when the field in enclosed by some arbitrary volume--such as the energy density inside the inductor coil (solenoids are inductors too).

$\eta=\frac{B^2}{2\mu_0\mu_r}$

Ref: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/indeng.html#c2

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  • $\begingroup$ But is Energy density = The amount of work that can be done? By the solenoid for example attracting another dipole? $\endgroup$ – Pupil Oct 21 '13 at 7:00
  • $\begingroup$ @Key yes indeed (if integrated over all space). Have a look at the little derivation in my answer here that tallys up energy input into a lossless system. The large currents that flow in a parallel LC circuit are shuttling energy to and fro between energy stored in the capacitor's electric field and energy stored in the magnetic field, and, in the lossless case, no energy leaves the system - the energy levels in the two circuit elements are half a period out of phase. $\endgroup$ – WetSavannaAnimal Oct 21 '13 at 9:38
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Imagine a magnet which produces a magnetic field B. The energy density means that the ratio of the magnetic energy and the volume in a certain space. If we put another magnet in the filed, this magnet will feel a potential due to the field or the energy around it. The amount of potential is related to energy density tightly.

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  • $\begingroup$ Is the potential energy = Energy density? This is way I'm confused. $\endgroup$ – Pupil Oct 21 '13 at 6:59
  • $\begingroup$ Energy density is density of energy.In this case, magnetic field is something we know unless we feel it. We can feel the field only if we feel the potential produced by the field energy. Even if we couldn't see the field, we know that the field fills all space. Since there's field, there's energy. Then energy density emerges. $\endgroup$ – ever_never Oct 29 '13 at 14:17

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