
### Cross product

Cross product is defined as

To find the direction of the vector $\vec {C}$, use the right-hand rule.

(a)
Place the first vector in the cross product $\vec {A}$ in the palm of your right hand, and the second vector $\vec {B}$ sticking out perpendicularly to your palm.
(b)
Sweep the fingers from vector $\vec {A}$ to $\vec {B}$ and your thumb will be pointing to the direction of the vector $\vec {C}$.

### Magnetic Force on a charged particle

Magnetic force on a charged particle $F=q \vec {v} \cross \vec {B}$ will change the direction of the particle’s path, perpendicularly to the direction of the magnetic field and the velocity vector. However, it will not change the speed of the particle. The magnetic field cannot accelerate a charged particle.

An electron moves with a constant speed $\vec {v}$ in vacuum in a presence of a magnetic field with flux density $\vec {B}$. The magnetic field can change

both the direction of $\vec {v}$, and $|\vec {v}|$ magnitude. neither the direction of $\vec {v}$, nor $|\vec {v}|$ magnitude. the direction of $\vec {v}$, but not $|\vec {v}|$ magnitude. not enough information

### Lorenz Force

The force on a charged particle in an electric and magnetic field, a Lorentz force, is

$q$ is the charge of the particle, $\vec {E}$ is the external electric field, $v$ is the particle’s velocity, and $\vec {B}$ is the magnetic field.

Here is an interesting applet that lets you see the charged particle’s path by setting the electric and magnetic fields’ strength, charge and mass of the particle, and the speed direction and magnitude.