Magnetic tension force
Encyclopedia
The magnetic tension force is a restoring force
(SI unit: Pa
·m
−1) that acts to straighten bent magnetic field lines. It equals:
It is analogous to rubber bands and their restoring force. The force is directed antiradially. Although magnetic tension is referred to as a force, it is actually a pressure gradient (Pa m−1) which is also a force density (N m−3).
The magnetic pressure
is the energy density
of the magnetic field and it increases as magnetic field lines convene with each other. In contrast, magnetic tension force is determined by how much the magnetic pressure changes with distance. Magnetic tension forces also rely on vector current densities
and their interaction with the magnetic field 
. Plotting magnetic tension along adjacent field lines can give a picture as to their divergence and convergence with respect to each other as well as current densities 
.
, where it controls dynamics of some systems and the shape of magnetized structures.
In magnetohydrodynamics
, the magnetic tension force can be derived from the momentum equation
using the relation
. The first term on the right hand side of the above equation represents electromagnetic forces and the second term represents pressure gradient forces.
Restoring force
Restoring force, in a physics context, is a variable force that gives rise to an equilibrium in a physical system. If the system is perturbed away from the equilibrium, the restoring force will tend to bring the system back toward equilibrium....
(SI unit: Pa
Pascal (unit)
The pascal is the SI derived unit of pressure, internal pressure, stress, Young's modulus and tensile strength, named after the French mathematician, physicist, inventor, writer, and philosopher Blaise Pascal. It is a measure of force per unit area, defined as one newton per square metre...
·m
Metre
The metre , symbol m, is the base unit of length in the International System of Units . Originally intended to be one ten-millionth of the distance from the Earth's equator to the North Pole , its definition has been periodically refined to reflect growing knowledge of metrology...
−1) that acts to straighten bent magnetic field lines. It equals:
It is analogous to rubber bands and their restoring force. The force is directed antiradially. Although magnetic tension is referred to as a force, it is actually a pressure gradient (Pa m−1) which is also a force density (N m−3).
The magnetic pressure
Magnetic pressure
Magnetic pressure is an energy density associated with the magnetic field. It is identical to any other physical pressure except that it is carried by the magnetic field rather than kinetic energy of the gas molecules. Interplay between magnetic pressure and ordinary gas pressure is important to...
is the energy density
Energy density
Energy density is a term used for the amount of energy stored in a given system or region of space per unit volume. Often only the useful or extractable energy is quantified, which is to say that chemically inaccessible energy such as rest mass energy is ignored...
of the magnetic field and it increases as magnetic field lines convene with each other. In contrast, magnetic tension force is determined by how much the magnetic pressure changes with distance. Magnetic tension forces also rely on vector current densities
and their interaction with the magnetic field . Plotting magnetic tension along adjacent field lines can give a picture as to their divergence and convergence with respect to each other as well as current densities .Use in Plasma Physics
Magnetic tension is particularly important in plasma physics and magnetohydrodynamicsMagnetohydrodynamics
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...
, where it controls dynamics of some systems and the shape of magnetized structures.
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...
, the magnetic tension force can be derived from the momentum equation
using the relation
. The first term on the right hand side of the above equation represents electromagnetic forces and the second term represents pressure gradient forces.