The anti-symmetric nature of the magnetic field's tensor representation is the fundamental mathematical reason why the resulting force on a charged particle is always perpendicular to both the field and the particle's velocity. It shows how the zero diagonal elements and the opposite-signed off-diagonal pairs in the tensor directly correspond to the rotational effect of the Lorentz force.
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$\complement\cdots$Counselor
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the force being perpendicular to both the velocity and the field as result of the tensor's anti-symmetric nature
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$\gg$Operations and Properties of Tensors
$\ggg$Mathematical Structures Underlying Physical Laws
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