E×B

The term "E×B" refers to the cross product of the electric field (E) and the magnetic field (B) in electromagnetism, often encountered in the context of the Lorentz force law. In physics, particularly in classical electromagnetism, the Lorentz force describes the force exerted on a charged particle moving through electric and magnetic fields. The magnetic component of this force is given by the vector cross product of the particle's velocity (v) with the magnetic field (B), resulting in a force perpendicular to both the velocity and the magnetic field. The electric field (E) contributes independently, acting along the direction of the field.

The notation E×B specifically appears in certain theoretical and applied contexts, such as in plasma physics, where the interaction between electric and magnetic fields plays a critical role in governing particle motion and energy transfer. For instance, in magnetohydrodynamics (MHD), the cross product E×B represents the electromagnetic force per unit volume, influencing fluid dynamics in conductive media like plasmas or liquid metals.

In practical applications, E×B drift is a phenomenon where charged particles in a plasma experience a net drift velocity due to the combined influence of perpendicular electric and magnetic fields. This drift arises because the electric field accelerates the particles, while the magnetic field bends their trajectories, resulting in a collective motion perpendicular to both fields. Such drifts are significant in fusion research, where controlling plasma behavior is essential for sustaining high-temperature reactions.

The mathematical expression for the E×B drift velocity is derived from the Lorentz force equation, where the electric force balances the magnetic force component parallel to the electric field, leaving a residual perpendicular motion. This concept is foundational in understanding plasma confinement in devices like tokamaks and stellarators, where maintaining stable plasma conditions is crucial for energy production.