Magnetic pressure

A gradient in field strength causes a force due to the magnetic pressure gradient called the magnetic pressure force.

In ideal magnetohydrodynamics (MHD) the magnetic pressure 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.

[1][2] 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.

The magnetic pressure force is readily observed in an unsupported loop of wire.

This gradient in field strength gives rise to a magnetic pressure force that tends to stretch the wire uniformly outward.

At even higher currents, the magnetic pressure can create tensile stress that exceeds the tensile strength of the wire, causing it to fracture, or even explosively fragment.

Thus, management of magnetic pressure is a significant challenge in the design of ultrastrong electromagnets.

Magnetic pressure can also be used to propel projectiles; this is the operating principle of a railgun.

If non-magnetic forces are also neglected, the field configuration is referred to as force-free.

Furthermore, if the current density is zero, the magnetic field is the gradient of a magnetic scalar potential, and the field is subsequently referred to as potential.