Magnetic fields have a big effect on how charged particles, like electrons, move around. This is explained by something called the Lorentz force law.

When a charged particle (think of an electron with a charge, $q$) enters a magnetic field (which has a strength known as magnetic flux density, $B$), it feels a magnetic force. This force can be shown with this simple formula:

$$F = q(v \times B)$$

In this formula, $v$ is the speed of the particle. The magnetic force always acts at a right angle to both the direction the particle is moving and the direction of the magnetic field. This means instead of going in a straight line, the particle moves in a circular or spiral path.

Important Points to Remember:

• Direction of Force: You can figure out which way the force is pushing by using the right-hand rule.

• Radius of Motion: The size of the circular path (called the radius, $r$) can be found using this formula:

$$r = \frac{mv}{qB}$$

In this, $m$ represents the mass of the particle.

• Frequency of Motion: The frequency (how often the particle goes around in its circle, called cyclotron frequency $f$) is calculated by:

$$f = \frac{qB}{2\pi m}$$

All of these ideas show how magnetic fields can control charged particles. This is really useful in things like particle accelerators and in keeping particles together in fusion reactors.