u/Atik99X

Lorentz Force is defined as the total force experienced by a particle when passing through both electric and magnetic fields. The equation of Lorentz force is given by:

F = F_e + F_m

Where,

F_e = e.E

F_m = e(v × B)

F = e.E + e(v × B)

= e(E + v × B)

e = charge of moving electron

E = source electric field

v = velocity of electron

B = source magnetic field

Can you give a real life example? Well atom is a standard example but I need some more.

Since the electron is a fast particle rules SR should be applied. I didn't understand the exact scenario. There were mentioned two frames on S and other S`, which frame remained stationary and which was moving.