Why do charged particles spiral in magnetic fields?

Charged particles spiral in magnetic fields due to the Lorentz force acting perpendicular to their velocity and the magnetic field.

The motion of charged particles in magnetic fields is governed by the Lorentz force law. This law states that the force (F) acting on a charged particle in a magnetic field is equal to the charge (q) of the particle multiplied by the velocity (v) of the particle and the magnetic field (B), and is always perpendicular to the direction of motion and the magnetic field. Mathematically, this is represented as F = qvB sinθ, where θ is the angle between the velocity and the magnetic field.

When a charged particle enters a magnetic field, it experiences a force that is always perpendicular to its direction of motion. This force does not change the speed of the particle, but constantly changes its direction, causing it to move in a circular or spiral path. The direction of the force (and hence the direction of the spiral) depends on the sign of the charge. Positive charges spiral in one direction, while negative charges spiral in the opposite direction.

The radius of the spiral path is determined by the mass and speed of the particle, the charge of the particle, and the strength of the magnetic field. The faster the particle or the stronger the magnetic field, the smaller the radius of the spiral. Conversely, the heavier the particle or the weaker the magnetic field, the larger the radius of the spiral.

In summary, the spiralling motion of charged particles in magnetic fields is a direct result of the Lorentz force, which acts perpendicular to the velocity of the particle and the magnetic field. This force constantly changes the direction of the particle, causing it to move in a spiral path. The properties of this path are determined by the characteristics of the particle and the magnetic field.