The force that affects the motion of objects in a magnetic field is called the Lorentz force. This force acts on charged particles moving through a magnetic field. The magnet's influence depends on the charge of the particle, its velocity, and the strength of the magnetic field. Mathematically, the Lorentz force is described by the equation F = q(v × B), where F is the force, q is the charge, v is the velocity vector, and B is the magnetic field vector. This principle is fundamental to understanding electromagnetic interactions.