Magnetic tension
In physics, magnetic tension is a restoring force with units of force density that acts to straighten bent magnetic field lines. The force density (in SI) formula_1 exerted perpendicular to a magnetic field formula_2 can be expressed as formula_3 where formula_4 is the vacuum permeability. 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. Magnetic tension is analogous to the restoring force of rubber  bands. Plasma physics. Magnetic tension is particularly important in plasma physics and magnetohydrodynamics (MHD), where it controls dynamics of some systems and the shape of magnetic structures. Derivation. Magnetohydrodynamic equations. In MHD, the magnetic tension force can be derived from the Cauchy momentum equation: formula_5 The first term on the right hand side of the above equation represents the Lorentz force and the second term represents pressure gradient forces. Using Ampère's law, formula_6, and the vector identity formula_7 we obtain the following equation: formula_8 The first and last gradient terms are associated with the total pressure which is the  sum of the magnetic and thermal pressures; formula_9. The second term represents the magnetic tension. We can separate the force due to changes in the magnitude of formula_2 and its direction by writing formula_11 with formula_12 and formula_13 a unit vector. Some vector identities give formula_14 The first term is the magnetic pressure due solely to changes in formula_15 in directions perpendicular to formula_2, while the second term is the "tension" due solely to changes in the direction of formula_2 (or curvature of magnetic field lines). Maxwell stress tensor. A more rigorous way to look at this is through Maxwell  stress tensor. The Lorentz force equation formula_18 gives the force per unit volume: formula_19 This, after some algebra and using Maxwell's equations to replace the current, leads to formula_20 This result can be re-written more compactly by introducing the Maxwell stress tensor, formula_21 All but the last term of the above expression for the force density, formula_22, can be written as the divergence of the Maxwell tensor: formula_23 which gives the electromagnetic force density in terms of Maxwell stress tensor, formula_24, and the Poynting vector, formula_25. Now, the magnetic tension is implicitly included inside formula_24. The implication of  the above relation is the conservation of momentum. Here, formula_27 is the momentum flux density and plays a role similar to formula_28 in Poynting's theorem.