Is the Lorentz force just the combination of the two mag fields of a permanent mag and current

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Joined Jun 28, 2018
When we have a moving charge (current) moving perpendicularly through a magnetic field a force will act on that charge. This is illustrated in the first diagram below with a coil of wire turning in a magnetic field. We can determine the direction of the turning coil by using flemming's left hand motor rule. This is illustrated in the second diagram. Without getting into heavy details (cross product, calculus etc.) is the force causing the coil to turn called the Lorentz force? And is the Lorentz force actually caused by the interacting magnetic fields of the permanent magnet and the current through the coil? (This is illustrated in the second diagram using Maxwell's Right Hand corkscrew rule. The magnetic field of the current carrying wire is in the same direction at the top part of the permanent field and in opposite direction at the bottom part. This aids the top part and cancels the bottom part causing a force to be exerted on the wire pushing it down)

In other words, are the Lorentz force and the force caused by combining/cancelling the magnetic fields of the permanent magnet and current carrying wire the same force, or are the different from each other and should be thought of separately?