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v×B is the vector cross product of a particle’s velocity v and a magnetic field B, yielding a vector perpendicular to both v and B. The magnitude is |v×B| = v B sin θ, where θ is the angle between v and B. The direction is given by the right-hand rule: point the fingers of your right hand in the direction of v, curl toward B, and the thumb points in the direction of v×B.

In the Lorentz force law, the magnetic component of the force on a charged particle is F_mag = q (v×B). For a positive charge, F aligns with v×B; for a negative charge, it points opposite. Because the magnetic force is perpendicular to the particle’s instantaneous velocity (in the absence of an electric field), it does no work on the particle and changes only the direction of motion. This leads to circular motion in a uniform magnetic field, with radius r = m v/(q B) and angular frequency ω = q B/m. In nonuniform fields, the motion can become more complex, including helical trajectories and magnetic drifts.

v×B vanishes if v is parallel to B (or if B is zero), in which case there is no magnetic force on the particle. In SI units, B is measured in teslas and v in meters per second, with |F| = |q| v B sin θ for the magnetic force on a point charge. The concept also appears in broader contexts, such as plasma physics and devices like spectrometers and cyclotrons, where current densities j interact with B via j×B.