Lorentz Force

In physics (specifically in electromagnetism) the Lorentz force (or electromagnetic force) is the force exerted on a charged particle q moving with velocity v through an electric field E and magnetic field B. The Lorentz force is the combination of the electric and magnetic force on a point charge due to electromagnetic fields.
The entire electromagnetic force F on the charged particle is called the Lorentz force (after the Dutch physicist Hendrik A. Lorentz) and is given by
$$\bbox[5px,border:1px solid red] {\color{blue}{\textbf{F} = q\textbf{E} + q\textbf{v} \times \textbf{B}}} \tag{1}$$
In terms of the angle $\phi$ between velocity and magnetic field, eq. 1 is given as
$$\bbox[5px,border:1px solid red] {\color{blue}{\textbf{F} = q\textbf{E} + q\textbf{v} \textbf{B} sin \phi}} \tag{2}$$
The first term the equation (1) is contributed by the electric field. The second term is the magnetic force and has a direction perpendicular to both the velocity and the magnetic field. The magnetic force is proportional to q and to the magnitude of the vector cross product $v \times B$. In terms of the angle $\phi$ between v and B, the magnitude of the force equals $qvB sin \phi$.
Lorentz Force Law: Right Hand Rule.
Fig. 1:Lorentz Force Law: Right Hand Rule.
The magnetic force on a moving charge reveals the sign of the charge carriers in a conductor. A current flowing from right to left in a conductor can be the result of positive charge carriers moving from right to left or negative charges moving from left to right, or some combination of each.
When a conductor is placed in a B field perpendicular to the current, the magnetic force on both types of charge carriers is in the same direction. This force gives rise to a small potential difference between the sides of the conductor. Known as the Hall effect, this phenomenon (discovered by the American physicist Edwin H. Hall) results when an electric field is aligned with the direction of the magnetic force.
The Hall effect shows that electrons dominate the conduction of electricity in copper. In zinc, however, conduction is dominated by the motion of positive charge carriers. Electrons in zinc that are excited from the valence band leave holes, which are vacancies (i.e., unfilled levels) that behave like positive charge carriers. The motion of these holes accounts for most of the conduction of electricity in zinc.

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