Lorentz force as the gradient of a scalar quantity and the MHD flow under force-free magnetic field in elliptic cylinder coordinates system

In the present paper the representation of Lorentz force as the gradient of a scalar quantity in the elliptic cylindrical co-ordinates, neglecting the effects of displacement current is attempted. Under some assumptions the scalar quantity representing the Lorentz force is given by psi=A[(cosh-1 u)2 + (sin-1v)2]Zsup(2n)/(u2 - v2). An attempt has also been made to find an expression for the force-free field in elliptic cylindrical system of co-ordinates. Since the MHD flow under force-free magnetic field becomes Beltrami flow, the expression for the pressure in such a flow has also been attempted. It has also been shown that the velocity of the flow is constant along the curve (cosh-1u, cos-1u, 0). (author)