How do charged particles move within magnetic fields?

Charged particles move in a circular path perpendicular to the magnetic field they are in.

When a charged particle enters a magnetic field, it experiences a force known as the Lorentz force. This force is always perpendicular to the direction of motion of the particle and to the direction of the magnetic field. As a result, the particle moves in a circular path within the magnetic field, with the plane of the circle being perpendicular to the direction of the field.

The direction of motion of the particle is determined by the right-hand rule. If you point your right thumb in the direction of the particle's velocity and your fingers in the direction of the magnetic field, your palm will point in the direction of the force on a positive charge. For a negative charge, the force is in the opposite direction.

The radius of the circular path is determined by the charge and speed of the particle, the mass of the particle, and the strength of the magnetic field. The greater the charge or speed of the particle, or the stronger the magnetic field, the smaller the radius of the path. Conversely, the greater the mass of the particle, the larger the radius.

The particle continues to move in this circular path until it exits the magnetic field or until another force acts upon it. If the particle's velocity is parallel or antiparallel to the magnetic field, it will not experience a magnetic force and will continue in a straight line.

The speed of the particle does not change as it moves within the magnetic field, because the magnetic force does no work on the particle. This is because the force is always perpendicular to the direction of motion, so the dot product of the force and the displacement is zero. Therefore, the kinetic energy of the particle remains constant.

In summary, charged particles move in a circular path within a magnetic field, with the plane of the circle being perpendicular to the field. The direction of motion is determined by the right-hand rule, and the radius of the path is determined by the properties of the particle and the field. The speed of the particle remains constant.