Magnetic Field & Lorentz Force Explorer (2D)

This 2D companion builds the same field-and-force physics as the 3D version from scratch on a flat canvas: place up to four current loops anywhere on the stage, sum their fields with a discretized Biot-Savart integral into a live contour map, then launch a charged test particle and watch its path bend in real time under the true Lorentz force F=qv×B, numerically integrated every frame rather than following a scripted arc. Because a planar current loop's field at any point in its own plane is exactly perpendicular to that plane, the simulation needs only a single scalar field B_z(x,y) to get the force exactly right — no shortcuts, no decorative field lines. Drag loops to reshape the field, click one to reverse its current, and watch the particle's curvature radius shrink where the summed field is strong and straighten where opposing loops cancel it out.