Geometric Model of Circular Magnetic Field

This applet demonstrates geometric and vector constructions within a circular magnetic field environment. Through the use of fundamental geometric objects including points, lines, circles, arcs, line segments, orthogonal lines, and vectors, it builds a comprehensive geometric model of a circular magnetic field. The model serves as an interactive teaching tool for visualizing how charged particles move under the influence of a magnetic field. Students can observe and trace the trajectories that charged particles follow when entering a circular magnetic field region, gaining insight into the relationship between velocity direction, magnetic field orientation, and the resulting curved paths. The applet illustrates the direction of the Lorentz force acting on moving charges, showing how this force is always perpendicular to both the particle velocity and the magnetic field direction, consistent with the right-hand rule. It also highlights various geometric intersection and orthogonality relationships that arise in the construction, such as the perpendicularity between the Lorentz force direction and the instantaneous velocity vector, the radial nature of centripetal acceleration in uniform circular motion, and the geometric properties of tangent and normal lines at points of intersection between particle paths and the magnetic field boundary. By interactively manipulating parameters such as the particle entry point, initial velocity direction, and field strength, students can explore how different conditions affect the trajectory shape and exit behavior. This hands-on exploration bridges the gap between abstract electromagnetism theory and concrete geometric visualization, making it particularly valuable for physics and mathematics students studying charged particle motion in magnetic fields, electromagnetic theory, and applied geometry.