Current flow ($I$) and the electric force responsible in moving the charges are proportional to the Lorentz force acting on those charge due to the magnetic field that the current flow produces, all based on the definition of the Lorentz force
$$ F_L = IL \times B$$
However, I'm curious if they are equal or greater/less than one another. My assumption is it all depends on the design of the circuit and the resistance defined. The circuit can be very very low in resistance(yielding in high conductivity) and the force required(and work) to move the charge could be low.
I'm trying to see if I'm missing something with the following statement:
$$F_E \propto F_L$$
...Are the magnitudes necessarily equal? Or only proportional?
Rectangular loop with current flow, with 4 sides, how side 1 is experiencing a force from the external magnetic fields of 2,3,4.