How is the path of a charged particle in a magnetic field determined?

The path of a charged particle in a magnetic field is determined by the Lorentz force.

When a charged particle moves through a magnetic field, it experiences a force perpendicular to both its velocity and the magnetic field direction. This force is known as the Lorentz force and is given by F = q(v x B), where q is the charge of the particle, v is its velocity, and B is the magnetic field.

The direction of the Lorentz force is determined by the right-hand rule. If the thumb of the right hand points in the direction of the velocity of the particle and the fingers point in the direction of the magnetic field, then the palm of the hand will point in the direction of the force.

The magnitude of the Lorentz force depends on the charge of the particle, its velocity, and the strength of the magnetic field. If the magnetic field is uniform, the particle will move in a circular path with a radius given by r = mv/qB, where m is the mass of the particle.

If the magnetic field is not uniform, the particle will experience a force that varies in direction and magnitude as it moves through the field. In this case, the path of the particle will be more complex and may be determined using numerical methods or approximations.

In summary, the path of a charged particle in a magnetic field is determined by the Lorentz force, which depends on the charge of the particle, its velocity, and the strength of the magnetic field. The direction of the force is given by the right-hand rule, and the path of the particle may be circular or more complex depending on the uniformity of the magnetic field.