Electromagnetic Attraction

William Sturgeon's original horseshoe electromagnet, from https://en.wikipedia.org/wiki/William_Sturgeon#/media/File:Sturgeon_electromagnet.png

Energy is conserved

Electrical engineers are routinely taught, correctly, that energy is conserved in electromagnets as far as forces of magnetic attraction are concerned.

Fig 3.23 — Magnetic pull between two iron surfaces.
(Figure from Electrical Technology, Edward Hughes, Longmans, Second Edition, 1966, p92)

The usual textbook approach is generally as shown in Figure 3.23 above, where conservation is assumed between electromagnetic and mechanical energy, in order to derive a formula for the attractive force between two magnetised ferromagnetic surfaces. Since experimental results for the force agree with this theoretical approach, the assumption is validated.

Force formula derivation

The formula for attractive force between the two adjacent surfaces in the above figure is derived like this:—

D and E are end portions of a one-piece laminated flexible ferromagnetic core, of cross-sectional area A, wound with coil C, carrying current I, which produces flux density B in the airgap of width g.  Then:

        Energy stored per cubic meter of airgap = B²/2μ₀ joules.

Force P balances the magnetic force of attraction between the surfaces of D and E. Suppose E is moved a small distance dg away from D, and also that I is increased simultaneously to keep B unaltered. Then from Faraday's Law and Lenz's Law, no e.m.f. will have been induced in C, and no energy will have been exchanged between the electric circuit and the magnetic circuit. Hence, all energy stored in the additional volume of airgap A × dg must have been derived from the work done when a force of magnitude P acted through a distance dg, i.e:

        P × dg = (B²/2μ₀)× A × dg

  So  P = B²A/2μ₀ newtons.

I'll just state, without proving it here, that energy is also always conserved regarding the energy taken from the electrical source to produce the magnetic field in the varying-volume airgap.

So there seems to be no possibility of over-unity performance from electromagnetic attraction alone.

What if a permanent magnet is added?

However, I will also raise, but not answer the question of whether energy is still conserved overall if a permanent magnet is added into the attracting magnetic circuit discussed above — especially if the (ferro)magnetic circuit is still not quite driven into magnetic saturation by the energised coil and the permanent magnet combined.

I'll look further at that question in future. In particular, in a future post I'll look at what seems likely to have been an over-unity device invented by the very orthodox and prestigious EPRI (Electric Power Research Institute), that exploited this idea as part of its operating principle.

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A cut-away view of an industrial switched-reluctance motor. The operating principle of all such motors relies on electromagnetic attraction. Analysis of switched-reluctance motor operation assumes (correctly) that energy is conserved overall.
Image from Electronic Control of Switched Reluctance Motors, Edited by TJE Miller, Newnes, 2001.