Magnetic Forces

Magnetic Lorentz force on currents and charges, Hall effect, and electric motor principles.

General idea of the topic

This block studies how an external magnetic field exerts force on moving charges and on currents in conductors, determining circular, helical trajectories and mechanical equilibria.

It analyses the Lorentz force on charged particles, the force on straight current-carrying conductors and the interaction between parallel conductors, always with vector control and dimensional validation.

What you will truly understand

• How to calculate the force on a moving point charge within a magnetic field.
• How to determine the force on a straight conductor carrying current.
• How to predict the interaction between parallel conductors with currents.
• How to interpret the radius of gyration and cyclotron frequency of charged particles.

Recommended learning route

1. Magnetic force on a moving charge.
2. Force on a current-carrying conductor.
3. Force between parallel conductors.

Physical criterion you must acquire

The magnetic force is always perpendicular to the velocity: it does no work, only changes direction. Verify the cross product and right-hand rule before interpreting the result.

Connection with real problems

Electric motors, galvanometers, mass selection in spectrometry, particle accelerators and loudspeakers.

Final goal of the topic

Solve magnetic force problems with vector control, sign coherence and kinematic domain validation.