# Magnetic attraction between infinite current sheets

• particlezoo
In summary: So fields store potential energy. The more concentrated the field, the more potential energy is stored. And the more potential energy is stored, the more energy the field will generate.
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

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.

mfb said:
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.

Ok.

## 1. What is the concept of magnetic attraction between infinite current sheets?

The concept of magnetic attraction between infinite current sheets is based on the interaction between two parallel sheets of infinite length carrying current in the same direction. This phenomenon is governed by the Biot-Savart law, which states that the magnetic field produced by a current-carrying conductor is directly proportional to the magnitude of the current and inversely proportional to the distance from the conductor.

## 2. How is the strength of magnetic attraction between infinite current sheets determined?

The strength of magnetic attraction between infinite current sheets is determined by the distance between the sheets and the magnitude of the currents flowing through them. As the distance between the sheets decreases, the magnetic field strength increases, resulting in a stronger magnetic attraction between the sheets.

## 3. What factors affect the magnetic attraction between infinite current sheets?

The magnetic attraction between infinite current sheets is affected by the magnitude of the currents, the distance between the sheets, and the relative orientation of the sheets. If the currents are flowing in opposite directions, the sheets will repel each other instead of attracting.

## 4. Can the magnetic attraction between infinite current sheets be used for practical applications?

Yes, the magnetic attraction between infinite current sheets has several practical applications. It is used in various devices such as electric motors, generators, and magnetic levitation trains. It is also an important concept in electromagnetic induction, which is the basis of many electrical devices.

## 5. How does the magnetic attraction between infinite current sheets compare to that of point charges?

The magnetic attraction between infinite current sheets is similar to the electrostatic attraction between point charges in that both are governed by inverse square laws. However, unlike point charges, the magnetic field produced by infinite current sheets is always perpendicular to the direction of the current flow, resulting in a different pattern of attraction and repulsion between the sheets.

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