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I know the equation for Lorentz's force:

$$\vec{F_B}=I\vec{dl}\times\vec{B}$$

In class I was told that here, the magnetic field is created by another current-carrying wire, but could it be just caused by a moving point charge?

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Yes, the only requirement is that there is another current. This can be a current-carrying wire as you said, but also a moving point charge.
A moving point charge is a current, as you can see from the definition of a current: \begin{equation} I = \frac{\Delta q}{\Delta t}. \end{equation} The $q$ here is just some charge, no matter how it arrived there.

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