洛伦兹力不做功

What? The Lorentz force does no work? It may seem crazy for a moment; after all, why should we care about a force that does no work? It turns out that the explanation is actually very simple, and that the Lorentz force is still very important.

Let us suppose that we have a charge $q$ with velocity $\vec{v}$ and a magnetic field $\vec{B}$ at the location of the particle. From the definition of the Lorentz force, we have: $$\vec{F}=q(\vec{v}\times\vec{B})$$ Now, just think about what we know about cross products. The cross product of $\vec{v}$ and $\vec{B}$ will be perpendicular to both the velocity vector and the magnetic field vector. Thus, the Lorentz force is perpendicular to the velocity, meaning that the dot product $\vec{F}\cdot\vec{dr}=0$, where $\vec{dr}$ is the displacement vector. Therefore, the force does not do any work!

This conclusion is exceedingly simple, but it is one that throws many people off, just due to the nonintuitive notion that a force may never do any work at all.