Driven dynamic mode splitting of the magnetic vortex translational resonance

Eddy currents can produce significant drag on motion, called magnetic damping. For instance, when a metallic pendulum bob swings between the poles of a strong magnet, significant drag acts on the bob as it enters and leaves the field, quickly damping the motion.
If, however, the bob is a slotted metal plate, the magnet produces a much smaller effect. When a slotted metal plate enters the field, an emf is induced by the change in flux; however, it is less effective because the slots limit the...

A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a constant velocity. Like the electric field, the magnetic field at any point is directly proportional to the magnitude of the charge and inversely proportional to the square of the distance between the source point and the field point. However, unlike the electric field, the magnetic field is always perpendicular to the plane containing the line...

The number of nuclear spins aligned in the lower energy state is slightly greater than those in the higher energy state. In the presence of an external magnetic field, as the spins precess at the Larmor frequency, the excess population results in a net magnetization oriented along the z axis. When a pulse or a short burst of radio waves at the Larmor frequency is applied along the x axis, the coupling of frequencies causes resonance and flips the nuclear spins of the excess population from the...

In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis,  the precessing magnetic moments are randomly oriented around the z-axis. This...

The most common application of magnetic force on current-carrying wires is in electric motors. These consist of loops of wire, which are placed between the magnets with a magnetic field. When current flows through the loops, the magnetic field applies torque, which causes the shaft to rotate, thus converting electrical energy to mechanical energy.
Consider a rectangular current-carrying loop containing N turns of wire, placed in a uniform magnetic field. The net force on a current-carrying loop...

Consider a circular loop with a radius a, that carries a current I. The magnetic field due to the current at an arbitrary point P along the axis of the loop can be calculated using the Biot-Savart law.