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where φ(r, t) is the electric potential and A(r, t) is the magnetic potential, for an arbitrary source of charge density ρ(r, t) and current density J(r, t), and is the D'Alembert operator.
Biot–Savart law, in electromagnetics, it describes the magnetic field set up by a steady current density.
where subscripts and denote partial derivatives with respect to and , is the Josephson penetration depth, is the Josephson plasma frequency, is the so-called characteristic frequency and is the bias current density normalized to the critical current density .
In addition to hydrodynamical forces such as pressure and gravity, an element of magnetized fluid also feels the Lorentz force where is the current density and is the magnetic field vector.