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Lorentz force

A charged particle moving through electric and magnetic fields experiences the Lorentz force:

$$\mathbf F=q(\mathbf E+\mathbf v\times\mathbf B).$$

The electric and magnetic contributions behave differently.

Electric part

The electric force is

$$\mathbf F_E=q\mathbf E.$$

For a positive charge it points with the electric field; for a negative charge it points opposite.

Magnetic part

The magnetic force is

$$\mathbf F_B=q,\mathbf v\times\mathbf B.$$

Its magnitude is

$$F_B=|q|vB\sin\theta.$$

It vanishes when the particle moves parallel to the magnetic field and is largest for perpendicular motion.

Magnetic force changes direction, not speed

Because $\mathbf F_B$ is perpendicular to $\mathbf v$, an ideal magnetic force does no work on a point charge. It can bend the trajectory without changing the particle's kinetic energy.

For perpendicular uniform fields, this can produce circular motion. The sign of $q$ reverses the force direction given by the cross product.