A current sheet is an electric current

Electric current

Electric current is a flow of electric charge through a medium.This charge is typically carried by moving electrons in a conductor such as wire...

 that is confined to a surface, rather than being spread through a volume of space. Current sheets feature in magnetohydrodynamics

Magnetohydrodynamics

Magnetohydrodynamics is an academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water or electrolytes...

 (MHD), the study of the behavior of electrically conductive fluids: if there is an electric current through part of the volume of such a fluid, magnetic forces tend to expel it from the fluid, compressing the current into thin layers that pass through the volume.

The largest occurring current sheet in the Solar System

Solar System

The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...

 is the so-called Heliospheric current sheet

Heliospheric current sheet

The heliospheric current sheet is the surface within the Solar System where the polarity of the Sun's magnetic field changes from north to south. This field extends throughout the Sun's equatorial plane in the heliosphere. The shape of the current sheet results from the influence of the Sun's...

, which is about 10,000 km thick, and extends from the Sun

Sun

The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 and out beyond the orbit of Pluto

Pluto

Pluto, formal designation 134340 Pluto, is the second-most-massive known dwarf planet in the Solar System and the tenth-most-massive body observed directly orbiting the Sun...

.

In astrophysical plasmas

Plasma (physics)

In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...

 such as the solar

Sun

The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...

 corona

Corona

A corona is a type of plasma "atmosphere" of the Sun or other celestial body, extending millions of kilometers into space, most easily seen during a total solar eclipse, but also observable in a coronagraph...

, current sheets may have an aspect ratio (breadth divided by thickness) as high as 100,000:1. By contrast, the pages of most books have an aspect ratio close to 2000:1. Because current sheets are so thin in comparison to their size, they are often treated as if they have zero thickness; this is a result of the simplifying assumptions of ideal MHD

Magnetohydrodynamics

Magnetohydrodynamics is an academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water or electrolytes...

. In reality, no current sheet may be infinitely thin because that would require infinitely fast motion of the charge carriers whose motion causes the current.

Current sheets in plasmas store energy by increasing the energy density of the magnetic field

Magnetic field

A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...

. Many plasma instabilities

Instability

In numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds...

 arise near strong current sheets, which are prone to collapse, causing magnetic reconnection

Magnetic reconnection

Magnetic reconnection is a physical process in highly conducting plasmas in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration...

 and rapidly releasing the stored energy. This process is the cause of solar flares and is one reason for the difficulty of magnetic confinement fusion

Magnetic confinement fusion

Magnetic confinement fusion is an approach to generating fusion power that uses magnetic fields to confine the hot fusion fuel in the form of a plasma. Magnetic confinement is one of two major branches of fusion energy research, the other being inertial confinement fusion. The magnetic approach is...

, which requires strong electric currents in a hot plasma.

Magnetic field of an infinite current sheet

An infinite current sheet can be modelled as an infinite number of parallel wires all carrying the same current. Assuming each wire carries current I, and there are N wires per unit length, the magnetic field can be derived using Ampère's law

Ampère's law

In classical electromagnetism, Ampère's circuital law, discovered by André-Marie Ampère in 1826, relates the integrated magnetic field around a closed loop to the electric current passing through the loop...

:


R is a rectangular loop surrounding the current sheet. In the two sides perpendicular to the sheet, since . In the other two sides, , so if S is one parallel side of the rectangular loop of dimensions L x W, the integral simplifies to:
Since B is constant due to the chosen path, it can be pulled out of the integral:
The integral is evaluated:
Solving for B, plugging in for I_enc (total current enclosed in path R) as I*N*L, and simplifying:
Notably, the magnetic field strength of an infinite current sheet does not depend on the distance from it.

The direction of B can be found via the right-hand rule

Right-hand rule

In mathematics and physics, the right-hand rule is a common mnemonic for understanding notation conventions for vectors in 3 dimensions. It was invented for use in electromagnetism by British physicist John Ambrose Fleming in the late 19th century....

.

A well-known one-dimensional current sheet equilibrium: Harris current sheet

Harris current sheet is a stationary solution to the Maxwell-Vlasov system. The magnetic field profile is given by