Narrow Results

I investigate the finite temperature Casimir effect for a charged and massless scalar field satisfying mixed (Dirichlet–Neumann) boundary conditions on a pair of plane parallel plates of infinite size. The effect of a uniform magnetic field, perpendicular to the plates, on the Helmholtz free energy and Casimir pressure is studied. The $\zeta$-function regularization technique is used to obtain finite results. Simple analytic expressions are obtained for the zeta function and the free energy, in the limits of small plate distance, high temperature and strong magnetic field. The Casimir pressure is obtained in each of the three limits and the situation of a magnetic field present between and outside the plates, as well as that of a magnetic field present only between the plates is examined. It is discovered that, in the small plate distance and high temperature limits, the repulsive pressure is less when the magnetic field is present between the plates but not outside, than it is when the magnetic field is present between and outside the plates.

A ferrofluid is a mixture that exhibits both magnetism and fluidity. This merit enables the ferrofluid to be used in a wide variety of areas. Here we show that a floating ferrofluid bridge can be induced between two separated boards under a balanced external magnetic field generated by two magnets, while a flying ferrofluid bridge can be induced under an unbalanced external magnetic field generated by only one magnet. The mechanisms of the ferrofluid bridges were discussed and the corresponding mathematical equations were also established to describe the interacting magnetic force between the ferro particles inside the ferrofluid. This work answered a basic question that, except for the well-known floating water bridges that are related to electricity, one can also build up a liquid bridge that is related to magnetism.