# Is an electromagnetic sail possible?

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"Sail" is already used for other modes of propulsion, but personally I don't care.

Computing by the flux through the loop holds in many cases. It suffices that the current is conserved over the turn, and then magnetic material doesn't change it. This hold in DC, as well as when the circuit is clearly smaller than a quarter wavelength. It would become uninteresting at higher frequency, when for instance a radiowave induces current in a reception antenna.

If you consider an electric motor or generator, they do have magnetic material and are computed by d(flux)/dt. In fact, it is highly desired (and achieved) that the machine's flux does not pass at the conductors, since the varying induction there would induce eddy currents in the copper, creating big losses. The conductor slots are designed to keep the flux and the induction away from the copper. Same for a transformer.

With equations: https://en.wikipedia.org/wiki/Maxwell%27s_equations

rot(E) = -d(B)/dt

holds always, whatever the materials and shapes, and so does

voltage = -d(flux)/dt

whether there is a metal around the loop or not, whether the flux passes through a core or not.

In some cases, for instance a straight antenna, the path closing a voltage loop isn't clear so this law becomes less useful. But in DC or at frequencies low enough, current paths are closed, and integrating the voltage along them is generally the fertile approach.

It seems that you contest my explanation of the effect of magnetic shield on an electric coil. Do you think that the magnetic shield has no effect on the coil?

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The shield diverts the flux away from the conductor, but this doesn't change the force on the loop+shield.

You proposed to check the induced electromagnetive force, and this is an excellent approach. A net force, hence power and energy, needs an emf as the loop moves, but an emf in the loop results from a variation of the flux, so a permanent force over the distance would need to accumulate more and more flux in the loop from a uniform external induction, which won't happen.

As a consequence, even with the shield, we get a force only from the change of external induction with the distance and position versus the planet, and because the variation happens over a long distance, the net force is small. The torque on a loop is more significant as a rotation changes the flux over a short path, and this torque is used by some spacecraft.

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I remain sceptical about the idea of magnetic flux applied to the electromagnetic sail. The concept of magnetic flux is derived from one of the electromagnetism equations: divergence B = 0 (1). This equation implies also the inexistence of magnetic monopole. However the articles that I cited in my first message describe the making of a magnetic monopole by the use of a magnetic shield. This fact induces me to believe that the concepts derived from the equation divergence B = 0 are not valuable when a magnetic shield is present.

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I remain sceptical about the idea of magnetic flux applied to the electromagnetic sail. The concept of magnetic flux is derived from one of the electromagnetism equations: divergence B = 0 (1). This equation implies also the inexistence of magnetic monopole. However the articles that I cited in my first message describe the making of a magnetic monopole by the use of a magnetic shield. This fact induces me to believe that the concepts derived from the equation divergence B = 0 are not valuable when a magnetic shield is present.

Can you point to any of the work in that article that is not based on, or violates, Maxwell's equations?

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Can you point to any of the work in that article that is not based on, or violates, Maxwell's equations?

No, there is no violation of Maxwell's laws. But these laws have been established many years before the discovery of superconductivity. The superconductive materials have a magnetic property very special : their magnetic susceptibility is equal to -1. This property implies that the superconductive materials are perfect magnetic shield. The fact that a volume can be hidden from a magnetic field is a new property no described by Maxwell's laws. The making of a magnetic monopole whereas it is forbidden by Maxwell's laws is the best demonstration.

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No, there is no violation of Maxwell's laws. But these laws have been established many years before the discovery of superconductivity. The superconductive materials have a magnetic property very special : their magnetic susceptibility is equal to -1. This property implies that the superconductive materials are perfect magnetic shield. The fact that a volume can be hidden from a magnetic field is a new property no described by Maxwell's laws. The making of a magnetic monopole whereas it is forbidden by Maxwell's laws is the best demonstration.

Except it is described by Maxwell's laws, if that's what they used to model the behavior (with a susceptibility of 0, not -1).

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Except it is described by Maxwell's laws, if that's what they used to model the behavior (with a susceptibility of 0, not -1).

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If you use Maxwell's equations to model something, then a claim that one of Maxwell's equations doesn't apply is nonsensical.

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If you use Maxwell's equations to model something, then a claim that one of Maxwell's equations doesn't apply is nonsensical.

The apparent nonsense is here:

- one of the Maxwell's equations (divergence B = 0) implies the nonexistence of the magnetic monopole (1),

- two teams of scientists have produced a magnetic monopole with the help of a magnetic shield (2) (3).

(2) Gomory, F. et al. Experimental realization of a magnetic cloak. Science 335, 1466 (2012)

(3) Prat-Camps, J. et al. A Magnetic Wormhole. Sci. Rep. 5, 12488; doi: 10.1038/srep12488 (2015)

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The apparent nonsense is here:

- one of the Maxwell's equations (divergence B = 0) implies the nonexistence of the magnetic monopole (1),

- two teams of scientists have produced a magnetic monopole with the help of a magnetic shield (2) (3).

(2) Gomory, F. et al. Experimental realization of a magnetic cloak. Science 335, 1466 (2012)

(3) Prat-Camps, J. et al. A Magnetic Wormhole. Sci. Rep. 5, 12488; doi: 10.1038/srep12488 (2015)

You've misunderstood theur discussion of monopoles. From ref (3)

"close to the opening the field resembles that of a disk of monopoles rather than a single one (1/d2) . These monopolar magnetic fields are an alternative to those obtained by exotic spin ices29 and other systems30. Our magnetic wormhole thus creates an illusion of a magnetic field coming out of nowhere."

It's still a dipole, but similar to the quasiparticle experiments in spin ices, it's a dipole with the two ends so far apart that they look quite like a monopole. Here it would be because the flux return in confined to the shielded area.

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I propose to get back to the central subject of the discussion.

Let a loop of electric current of which a part is covered by the magnetic shield. When this loop is located at the terrestrial equator, it undergoes two kinds of effect from the geomagnetic field: a force and a torque.

The Laplace force applied to the loop is: F = I B L with I intensity of the current, B magnetic induction, L length of the electric conductor. This equation shows that this force does not depend on the magnetic flux through the loop.

The other effect which the loop undergoes is a torque which depends on the magnetic flux. The loop of electric current will rotate in the magnetic field until the magnetic flux through the loop is maximal.

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Just a detail about superconductors: only the type I eject the flux. Unfortunately, their maximum current density is too small for most uses, which rely on type II superconductors. These have some losses and let the flux pass through.

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For your goal, the Laplace force isn't written with enough details as

F = I B L

because it's an interaction among vectors rather than scalars, and the result depends on vector directions.

If B and I are uniform, L is straight, B and IL are perpendicular and you're interested in the F component perpendicular to both, then F = I B L is good enough and simpler. But for instance if B is parallel to the wire, you get zero F, which already tells that this is a vector computation.

The proper expression is, where F, B and dL are vectors:

F = integral ( B X idL ) where I write X the vector product of B and dL, and the integral is over the circuit.

It's already a simplification where the circuit is thin; if not, we would integrate BXJdV everywhere, with J being the current density.

In DC or at low frequencies, charge accumulation is negligible so the current I is uniform over the circuit.

Then F = I * integral ( B X dL ).

In this topic, you aim a uniform B if I understand properly.

Then F = I * B X integral ( dL )

and without charge accumulation, the current flows only over a closed path where integral ( dL ) = 0

so F = 0.

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A nonzero F would appear when B varies along the circuit. With the geomagnetic field varying over huge distances, this effect on a small loop is tiny. But if you create the induction and change its direction from one loop side to the other, you get a force on a linear motor.

Or a nonzero F can result from a non-uniform I, which implies high frequencies. Observed with radiation pressure.

Or if you seek a torque, then the integral isn't B X dL anymore: you also multiply by the distance to the axis, and since the current can have one direction at one axis side and the reverse direction at the other side, motors rotate.

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Just a detail about superconductors: only the type I eject the flux. Unfortunately, their maximum current density is too small for most uses, which rely on type II superconductors. These have some losses and let the flux pass through.

For my goal, the superconductive material of the magnetic shield must be type I to be opaque with the magnetic field but does not have to support a strong density of current. The superconductive material of the ring must support a strong density of current and must thus be type II but does not need to be opaque with the magnetic field.

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It depends much on the loop current... To shield the geomagnetic field away, a ferromagnetic material was a good start, like mumetal or permalloy.

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It depends much on the loop current... To shield the geomagnetic field away, a ferromagnetic material was a good start, like mumetal or permalloy.

A part of the magnetic shield described in the two articles presented in my first message is made with a ferromagnetic material. The other part of the magnetic shield is made with a superconductive material.

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