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What is the magnetic Lorentz force acting on a particle with charge $q$ moving with velocity $\vec{v}$ in a magnetic field $\vec{B}$?

Study flashcard from the deck Gaokao essentials: original practice.

Answer

$\vec{F} = q(\vec{v} \times \vec{B})$, with magnitude $F = |q| v B \sin\theta$ where $\theta$ is the angle between $\vec{v}$ and $\vec{B}$.

Explanation

Because the force is always perpendicular to velocity ($\vec{F} \cdot \vec{v} = 0$), the magnetic field does no work on a moving charge and does not change its kinetic energy.

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