Why Lorentz Force is Wrong

By Johny Jagannath

In many textbook treatments of classical electromagnetism, the Lorentz force Law is used as the definition of the electric and magnetic fields E and B. To be specific, the Lorentz force is understood to be the following empirical statement:

The electromagnetic force F on a test charge at a given point and time is a certain function of its charge q and velocity v, which can be parameterized by exactly two vectors E and B, in the functional form: 

Source [1] 

My thoughts:

The term, qE is wrong and does not fit in with the Lorentz force which only depends on the magnetic field that a charged particle is placed in. If the charged particle or the magnet is not moving, Lorentz force is zero. If the charged particle loses its charge (zero charge), Lorentz force is zero. If the magnetic field B is zero, Lorentz force is zero. Hence, the correct equation for Lorentz force is:

                                           

where q is the charged particle, v_rel is the relative velocity between the charged particle and the magnetic field lines (given by B). It is irrelevant whether the magnet moves or the charged particle moves. All that matters is the relative velocity between the magnet (field lines) and the charged particle. 

However, authors in the mainstream continue to misrepresent the Lorentz force equation and arrive at the conclusion that in the charged particle frame, the magnetic force is zero by assuming v = 0, when clearly this v is never zero in either frame. In the charged particle frame, the charge is at rest, while the field lines B move at v. And in the magnet or wire frame, the magnetic field lines B are at rest and the particle moves at v. 

Here are some examples of misrepresentations: 

1. Scott Huges – Lecture
http://web.mit.edu/sahughes/www/8.022/lec10.pdf
Suppose we now examine this situation from the point of view of the charge (the “charge frame”). From the charge’s point of view, it is sitting perfectly still. If it is sitting still, there can be no magnetic force!

2. Richard Feynman – Lecture
http://www.feynmanlectures.caltech.edu/II_01.html#Ch1-S5
An observer who was riding along with the two charges, however, would see both charges as stationary, and would say that there is no magnetic field.