🧄The Lorentz Force and the Principle of Zero Work Done by a Magnetic Field

The magnetic force, always acting perpendicular to a charged particle's velocity, does no work on the particle, thus it cannot change the particle's speed or kinetic energy. This perpendicularity, determined by the cross product, only alters the particle's direction, causing it to follow curved or circular paths. Conversely, an electric field can exert a force parallel to the particle's motion, thereby performing work and changing the particle's speed and kinetic energy. For instance, particle accelerators utilize electric fields for increasing particle speed and magnetic fields for controlling the direction of the particle beam.

🎬3D Lorentz Force and Work Done

while both electric and magnetic fields can exert a force on a charged particle, only the electric field does work. The magnetic force is always perpendicular to the particle's direction of motion, meaning it can change the particle's path but cannot change its kinetic energy. This is why the "Total Work Done" only increases when the electric field is turned on.

3D Lorentz Force and Work Done

🖊️Mathematical Proof

The Lorentz Force and the Principle of Zero Work Done by a Magnetic Field | Proof and Derivationviadean on Notion