How does the velocity of a charged particle affect its path in a magnetic field?

The velocity of a charged particle affects its path in a magnetic field.

When a charged particle moves through a magnetic field, it experiences a force perpendicular to both its velocity and the magnetic field. 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 force is given by the right-hand rule, where the thumb points in the direction of the velocity, the fingers point in the direction of the magnetic field, and the palm shows the direction of the force.

The magnitude of the force depends on the velocity of the particle. If the velocity is perpendicular to the magnetic field, the force is at its maximum and the particle moves in a circular path. If the velocity is parallel to the magnetic field, there is no force and the particle moves in a straight line. If the velocity is at an angle to the magnetic field, the force is at an intermediate value and the particle moves in a helical path.

The radius of the circular path is given by r = mv/qB, where m is the mass of the particle. This equation shows that the radius is proportional to the velocity of the particle. Therefore, a higher velocity results in a larger radius and a lower velocity results in a smaller radius.

In conclusion, the velocity of a charged particle affects its path in a magnetic field by determining the magnitude and direction of the Lorentz force, which in turn determines the shape of the path.