Magnetic tension

In physics, magnetic tension is a restoring force with units of force density that acts to straighten bent magnetic field lines.

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.

[citation needed] Magnetic tension is analogous to the restoring force of rubber bands.

[1] In ideal magnetohydrodynamics (MHD) the magnetic tension force in an electrically conducting fluid with a bulk plasma velocity field

can be derived from the Cauchy momentum equation: where the first term on the right hand side represents the Lorentz force and the second term represents pressure gradient forces.

The Lorentz force can be expanded using Ampère's law,

, and the vector identity to give where the first term on the right hand side is the magnetic tension and the second term is the magnetic pressure force.

a unit vector: where the spatial constancy of the magnitude has been assumed

[2][1] Magnetic tension and pressure are both implicitly included in the Maxwell stress tensor.

Terms representing these two forces are present along the main diagonal where they act on differential area elements normal to the corresponding axis.

For example, in a homogeneous magnetic field and an absence of gravity, magnetic tension is the sole driver of linear Alfvén waves.