How does an electrically charged particle behave in electric and magnetic fields?

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 particular point is known, is calculated by the following formula: F = qE.

So, We determined that an electrically charged particle, which is in an electric field, moves under the influence of the Coulomb force.

Now consider the Hall effect. It was found experimentally that a magnetic field affects the motion of charged particles. The magnetic induction is equal to the maximum force that affects the velocity of such a particle from the side of the magnetic field. The charged particle moves at a unit velocity. If an electrically charged particle flies into a magnetic field at a given speed, then the force that acts on the side of the field will be perpendicular to the velocity of the particle and, accordingly, to the magnetic induction vector: F = q [v, B]. Since the force that acts on the particle is perpendicular to the speed of motion, then the acceleration given by this force is also perpendicular to the motion, is the normal acceleration. Accordingly, the rectilinear trajectory of motion will be bent when a charged particle hits 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 maximal.

Now we write down Newton's law II : 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 along the circumference of the radius. Thus, the period of revolution of a charged particle along a circle does not depend on the speed of motion. It should be noted that for an electrically charged particle trapped in a magnetic field, the kinetic energy is unchanged. Due to the fact that the force is perpendicular to the motion of the particle at any of the points of 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 motion of a charged particle in a magnetic field can be determined using the "rule of the left hand". To do this, it is necessary to place the left palm in such a way that four fingers indicate the direction of the speed of movement of the charged particle, and the lines of magnetic induction were directed to the center of the palm, in which case the bent at a 90 degree angle will show the direction of the force that acts on the positive A charged particle. In the event that the particle has a negative charge, the direction of the force will be opposite.

If an electrically charged particle falls into the region of 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 electrical component, and the second to the magnetic component.