# IllustrationCross 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 $$\boldsymbol{B}$$.

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