I Magnetic attraction between infinite current sheets

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1. Mar 5, 2016

particlezoo

It is my understanding that fields store potential energy. That applies to both magnetic as well as electric fields. I know that the energy density also increases with the square of the norm of their vector value (at each coordinate).

When I have an infinite current sheet, the math says[1] that it will generate magnetic fields that are uniform on each side the sheet. So if I have two such sheets, with identical currents pointing the same way, the magnet fields should cancel between the sheets, and they should add elsewhere.

My understanding is that these sheets should attract because they are composed of numerous lines of current, and these should attract each other. This remains the case even for an arbitrary charge/mass ratio, such that induction effects may be ignored.

Yet, if we replace the two infinite current sheets with two infinite sheets with opposite electric charge, the same attraction will result in cancellation of electric field lines, except between the sheets. This is the exact opposite of the case for magnetic field of two infinite current sheets.

It would seem that (1/2)B^2/mu_0 in the ordinary vacuum of space represents potential energy stored in the magnetic field that can be released as kinetic energy in the same direction as the charge carrier flow, while the same represents the negative value of the potential energy (i.e. a binding energy) that can be released as kinetic energy at right angles to the current density.

Is this a surprise to any of you? If not, how were you taught to think of this?

[1]https://en.wikipedia.org/wiki/Current_sheet

2. Mar 5, 2016

Staff: Mentor

Potential energy usually refers to a potential, so it does not apply to the energy density of electromagnetic fields.
Two current sheets that approach each other would see some induced resistance, slowing current flow. You increase the volume with field, but you reduce the current and therefore the field strength, that's where the energy comes from.
That does not happen with the charged plates.

3. Mar 5, 2016

particlezoo

Ok.

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