# Illustration **Cross product between velocity and magnetic field**

## Level 3

Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.

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Cross product \(\boldsymbol{v} \times \boldsymbol{B}\) between the velocity \(\boldsymbol{v}\) of a charged particle and the magnetic field \(\boldsymbol{B}\). Thus the magnetic force \(\boldsymbol{F}_{\text m}\) acts on the particle orthogonal to the velocity and magnetic field.

The magnitude \(|\boldsymbol{v} \times \boldsymbol{B}|\) of the cross product corresponds to the area enclosed by \(\boldsymbol{v}\) and \(\boldsymbol{B}\).