The Lorentz force describes the force calculated using electromagnetic theory, it is the same thing as the electromagnetic force.

see https://en.wikipedia.org/wiki/Lorentz_force

Dear Franz,

Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. If a particle of charge q moves with velocity v in the presence of an electric field E and a magnetic field B, then it will experience a force

F = qE + qv x B

Variations on this basic formula describe the magnetic force on a current-carrying wire (Laplace force), the electromotive force in a wire loop moving through a magnetic field , and the force on a charged particle which might be travelling near the speed of light (relativistic form of the Lorentz force).

Hoping this will be helpful,

Rafik

Electromagnetic fields have the power to both accelerate and rotate charges and exert both Electric and Magnetic forces on a point charge which is nothing but Lorentz Force!

   I have understood the question as to distinguish the electromagnetic force from the Lorentz force. The electromagnetic force is

        ∂bTab=FacJc

where the Lorentz force is only its spacelike projection, for a charge q

       F=q(E+ v x B)

    And sorry because I have the previous formula wrong, because the timelike projection is

      ∂t E= E.J

      Being E energy and E.J the scalar product of the electric field E per the density of current J. That is to say, a power. This is the difference between both concepts and repit my SORRY for writing so badly my last post.

There would have been nothing like magnetism without motion of electric charges (actually in closed loops). Motion is a relativistic concept (i.e. frame dependent).

Due to an unequal Lorentz contraction of the positive and the negative lines charges, an otherwise neutral current-carrying wire in S-frame  becomes charged as seen in S'-frame in relative motion to it. Thus, the force F' exerted on a moving charge q as seen in the S'-frame is of electrical origin.

But, due to Newton's third law, forces exist in pairs (of equal magnitude but opposite directions). Thus, by applying the force transformation rule to F', the force F obtained in the S-frame is of magnetic origin.

So, magnetism is the result of electrostatics plus relativity. This is actually what the Lorentz equation is telling us.

I hope you find this narrative useful.

Ibanga

I guess Lorentz force is something well defined as the force which acts on a charge in an electromagnetic field.  The electromagnetic force has probably a wider use.  It meaning may depend on the problem you are working with.

   Transforming electricity in magnetism or vice versa, is a fundamental characteristics of electrodynamics or electromagnetism. What is real is the electromagnetic field which in certain circumstances can be reduced to some components, no electricity or magnetism alone. The behaviour of the fields with respect the themself or with respect to the sources is given in Maxwell equations. This is called electromagnetism.

The motion of the electromagnetic sources within the fields through an initial action and the conservation sources (Noether's currents) is known as electrodynamics. In three dimensions the equation which models that is the Lorentz equation, but in four dimensions (covarinant Lorentz electrodynamics) the equations are extended in only one extra equation more. This is all that we have in electrodynamics, no more!

11 laws of conservation= 10 associated to the symmetries of the spacetime SO(3,1) + 1 electric charge associated to the abelian U(1) gauge group.

Thus there can be only one equation more for electrodynamics, besides the Lorentz' equation of motion.

www.electropedia.org

Area Electromagnetism / Electromagnetic concepts and quantities

IEV ref 121-11-20

en

Coulomb-Lorentz force

force F exerted on a particle having electric charge Q and velocity v , given by the relation

F = Q(E + v x B)

where E is the electric field strength and B the magnetic flux density

Note 1 – The component vector Q E is the Coulomb force.

Note 2 – The component vector Q v x B is the Lorentz force.

Dear Daniel,

You wrote: "The behaviour of the fields with respect the themself or with respect to the sources is given in Maxwell equations."

More precisely, the Maxwell equations give the induction equations between electric and magnetic fields at one local place and time.

For electromagnetic equations between sources and detectors at a distance, one needs the Jefimenko equations of retarded fields, or the Liétard-Wiechert equations, which take into account the retardation of the fields by the speed of light.

You wrote: "In three dimensions the equation which models that is the Lorentz equation".

If you mean by 'Lorentz equation', the 'Lorentz factor', that is not correct. It are precisely the equations by the retarded fields that give the solution, and this will only comply with the Lorentz factor in a restricted number of cases.

The reason is that the Lorentz factor followed as the result of transforms of light signals between inertial reference frames, whereas in electromagnetism, there is also induction, so that the emitted and received E-M signals are in many cases different from the Lorentz factor.

You also wrote: "in four dimensions (covariant Lorentz electrodynamics) the equations are extended in only one extra equation more."

Because of what I wrote above, the Lorentz cannot be used as a standard solution for E-M waves between inertial reference frames, and so, it is utterly wrong to use covariant Lorentz electrodynamics.

Moreover, it was clearly stated by Einstein, as deBroglie attested in his 1937 book, that, Special Relativity is solely applicable to light signals between inertial reference frames. Hence, they are not influence the very parameters of the objects in the reference frames themselves.

Hence, the measurements from one to another inertial reference frame are only giving apparent results w.r.t. the objects in the inertial reference frames. Therefore, 'time' cannot be affected at all.