An electrically charged particle is a particle that has a positive or negative charge. It can be both atoms, molecules, and elementary particles. When an electrically charged particle is in an electric field, the Coulomb force acts on it. The value of this force, if the value of the field strength at a specific point is known, is calculated by the following formula: F = qE.
So,
we determined that an electrically charged particle that is in an electric field moves under the influence of the Coulomb force.
Now consider the Hall effect. It was experimentally discovered that a magnetic field affects the movement of charged particles. Magnetic induction is equal to the maximum force that affects the speed of such a particle from the side of the magnetic field. A charged particle moves at a unit speed. If an electrically charged particle flies into a magnetic field at a given speed, then the force acting on the field side will be perpendicular to the particle velocity and, accordingly, the magnetic induction vector: F = q [v, B]. Since the force that acts on the particle is perpendicular to the speed of movement, the acceleration given by this force is also perpendicular to the movement, is normal acceleration. Accordingly, the rectilinear trajectory of motion will be bent when a charged particle enters a magnetic field. If the particle flies parallel to the lines of magnetic induction, then the magnetic field does not act on the charged particle. If it flies perpendicular to the lines of magnetic induction, then the force that acts on the particle will be maximum.
Now we write Newton’s II law: qvB = mv 2 / R, or R = mv / qB, where m is the mass of the charged particle, and R is the radius of the trajectory. From this equation it follows that the particle moves in a uniform field around a circle of radius. So, the period of revolution of a charged particle in a circle does not depend on the speed of movement. It should be noted that for an electrically charged particle that has fallen into a magnetic field, the kinetic energy is unchanged. Due to the fact that the force is perpendicular to the movement of the particle at any point on the trajectory, the force of the magnetic field that acts on the particle does not perform the work associated with the movement of the charged particle.
The direction of the force acting on the movement of a charged particle in a magnetic field can be determined using the "rule of the left hand." To do this, position the left palm so that four fingers indicate the direction of the speed of movement of the charged particle, well, and the lines of magnetic induction are directed to the center of the palm, in which case the thumb bent at an angle of 90 degrees will indicate the direction of the force, which acts positively charged particle. In the event that the particle has a negative charge, then the direction of the force will be opposite.
If an electrically charged particle falls into the region of the combined action of magnetic and electric fields, then a force called the Lorentz force will act on it: F = qE + q [v, B]. The first term in this case refers to the electric component, and the second to the magnetic component.