What determines the path of a charge in a magnetic field?

The path of a charge in a magnetic field is determined by the charge's velocity, magnitude, direction, and the field's strength.

In more detail, the motion of a charged particle in a magnetic field is governed by the Lorentz force law. This law states that the force experienced by a charged particle in a magnetic field is equal to the charge of the particle multiplied by its velocity and the magnetic field strength, and is always perpendicular to the plane formed by the velocity and the magnetic field vectors. This force is responsible for the curved path that the charged particle follows.

The direction of the force, and hence the direction of the path, is given by the right-hand rule. If you point your fingers in the direction of the velocity of the particle and curl them towards the direction of the magnetic field, your thumb will point in the direction of the force. For a positive charge, the force is in the direction of your thumb, while for a negative charge, it is in the opposite direction.

The radius of the path followed by the charged particle is directly proportional to its velocity and inversely proportional to the charge and the magnetic field strength. This means that a particle with a higher velocity or a lower charge or magnetic field strength will follow a path with a larger radius, while a particle with a lower velocity or a higher charge or magnetic field strength will follow a path with a smaller radius.

The shape of the path is also determined by the angle between the velocity of the particle and the magnetic field. If the velocity is parallel or anti-parallel to the magnetic field, the particle will move in a straight line, as there is no force acting on it. If the velocity is at an angle to the magnetic field, the particle will follow a helical path, with the axis of the helix along the direction of the magnetic field.

In summary, the path of a charge in a magnetic field is determined by a combination of the charge's velocity, its magnitude, the direction of its velocity relative to the magnetic field, and the strength of the magnetic field.