Charged particles. Ancient Greek myth or modern reality? Charged particle accelerators Electromagnetic blood velocity counters
Let a particle of mass m and charge e fly with speed v into the electric field of a flat capacitor. The length of the capacitor is x, the field strength is equal to E. Shifting upward in the electric field, the electron will fly through the capacitor along a curved path and fly out of it, deviating from the original direction by y. Under the influence of the field force, F = eE = ma, the particle moves accelerated vertically, therefore . The time of movement of a particle along the x axis at a constant speed. Then 
. And this is the equation of a parabola. That. a charged particle moves in an electric field along a parabola.
3. Movement of charged particles in a magnetic field.
Let's consider the movement of a charged particle in a magnetic field of strength N. The field lines are depicted by dots and are directed perpendicular to the plane of the picture (towards us).
A moving charged particle represents an electric current. Therefore, the magnetic field deflects the particle upward from its original direction of motion (the direction of motion of the electron is opposite to the direction of the current)
According to Ampere's formula, the force deflecting a particle at any section of the trajectory is equal to , current, where t is the time during which charge e passes along section l. That's why . Considering that , we get 
The force F is called the Lorentz force. The directions F, v and H are mutually perpendicular. The direction of F can be determined by the left hand rule.
Being perpendicular to the velocity, the Lorentz force changes only the direction of the particle's velocity, without changing the magnitude of this velocity. It follows that:
1. The work done by the Lorentz force is zero, i.e. a constant magnetic field does not do work on a charged particle moving in it (does not change the kinetic energy of the particle).
Let us recall that, unlike a magnetic field, an electric field changes the energy and speed of a moving particle.
2. The trajectory of a particle is a circle on which the particle is held by the Lorentz force, which plays the role of a centripetal force.
We determine the radius r of this circle by equating the Lorentz and centripetal forces:
Where .
That. The radius of the circle along which the particle moves is proportional to the speed of the particle and inversely proportional to the magnetic field strength.
The period of revolution of a particle T is equal to the ratio of the circumference S to the particle velocity v: . Taking into account the expression for r, we obtain . Consequently, the period of revolution of a particle in a magnetic field does not depend on its speed.
If a magnetic field is created in the space where a charged particle is moving, directed at an angle to its speed, then the further movement of the particle will be the geometric sum of two simultaneous movements: rotation in a circle with a speed in a plane perpendicular to the lines of force, and movement along the field with a speed . Obviously, the resulting trajectory of the particle will be a helical line.
4. Electromagnetic blood speed meters.
The operating principle of an electromagnetic meter is based on the movement of electric charges in a magnetic field. There is a significant amount of electrical charges in the blood in the form of ions.
Let us assume that a certain number of singly charged ions move inside the artery at a speed of . If an artery is placed between the poles of a magnet, the ions will move in the magnetic field.
For directions and B shown in Fig. 1, the magnetic force acting on positively charged ions is directed upward, and the force acting on negatively charged ions is directed downward. Under the influence of these forces, the ions move to the opposite walls of the artery. This polarization of arterial ions creates a field E (Fig. 2) equivalent to the uniform field of a parallel-plate capacitor. Then the potential difference in an artery U with diameter d is related to E by the formula. This electric field, acting on the ions, creates electric forces and, the direction of which is opposite to the direction and, as shown in Fig. 2.
The electromagnetic force acting on a charged particle consists of the forces acting from the electric and magnetic fields:
The force defined by formula (3.2) is called the generalized Lorentz force. Taking into account the action of two fields, electric and magnetic, they say that an electromagnetic field acts on a charged particle.
Let us consider the motion of a charged particle in an electric field alone. In this case, hereinafter it is assumed that the particle is non-relativistic, i.e. its speed is significantly less than the speed of light. The particle is affected only by the electrical component of the generalized Lorentz force 
. According to Newton's second law, a particle moves with acceleration:
,
(3.3)
which is directed along the vector 
in case of positive charge and against the vector 
in case of negative charge.
Let us examine the important case of the motion of a charged particle in a uniform electric field. In this case, the particle moves uniformly accelerated ( 
). The trajectory of a particle depends on the direction of its initial velocity. If the initial speed is zero or directed along the vector 
, the particle motion is rectilinear and uniformly accelerated. If the initial velocity of the particle is directed at an angle to the vector 
, then the trajectory of the particle will be a parabola. The trajectories of a charged particle in a uniform electric field are the same as the trajectories of freely (without air resistance) falling bodies in the Earth’s gravitational field, which can be considered uniform near the Earth’s surface.
Example 3.1. Determine the final speed of a particle with mass 
and charge 
, flying in a uniform electric field 
distance 
. The initial velocity of the particle is zero.
Solution. Since the field is uniform and the initial velocity of the particle is zero, the particle’s motion will be rectilinear and uniformly accelerated. Let us write down the equations of rectilinear uniformly accelerated motion with zero initial speed:
.
Let's substitute the acceleration value from equation (3.3) and get:
.
In a uniform field 
(see 1.21). Size 
called the accelerating potential difference. Thus, the speed that a particle gains when passing through an accelerating potential difference 
:
.
(3.4)
When moving in non-uniform electric fields, the acceleration of charged particles is variable, and the trajectories will be more complex. However, the problem of finding the speed of a particle passing through an accelerating potential difference 
, can be solved based on the law of conservation of energy. The energy of motion of a charged particle (kinetic energy) changes due to the work of the electric field:
.
Here formula (1.5) is used for the work of the electric field on charge movement 
. If the initial velocity of the particle is zero ( 
) or small compared to the final speed, we get: 
, from which formula (3.4) follows. Thus, this formula remains valid in the case of motion of a charged particle in a nonuniform field. This example shows two ways to solve physics problems. The first method is based on the direct application of Newton's laws. If the forces acting on the body are variable, it may be more appropriate to use the second method, based on the law of conservation of energy.
Now let's consider the movement of charged particles in magnetic fields. A change in the kinetic energy of a particle in a magnetic field could only occur due to the work of the Lorentz force: 
. But the work done by the Lorentz force is always zero, which means the kinetic energy of the particle, and at the same time the modulus of its velocity, do not change. Charged particles move in magnetic fields with constant velocities. If an electric field can be accelerating with respect to a charged particle, then a magnetic field can only be deflecting, that is, it can only change the direction of its movement.
Let us consider options for charge motion trajectories in a uniform field.
1. The magnetic induction vector is parallel or antiparallel to the initial velocity of the charged particle. Then from formula (3.1) it follows 
. Consequently, the particle will move rectilinearly and uniformly along the magnetic field lines.
or 
.
The Lorentz force is constant in magnitude and directed perpendicular to the speed and vector of magnetic induction. This means that the particle will move all the time in one plane. In addition, it follows from Newton’s second law that the acceleration of the particle will be constant in magnitude and perpendicular to the speed. This is possible only when the trajectory of the particle is a circle, and the acceleration of the particle is centripetal. Substituting the value of centripetal acceleration into Newton's second law 
and the magnitude of the Lorentz force 
, find the radius of the circle:
.
(3.5)
Note that the period of rotation of a particle does not depend on its speed:
.
to the initial velocity of the particle (Fig. 3.3). First of all, we note once again that the velocity of the particle in absolute value remains constant and equal to the value of the initial velocity 
. Speed 
can be decomposed into two components: parallel to the magnetic induction vector 
and perpendicular to the magnetic induction vector 
.It is clear that if a particle flew into a magnetic field with only a component 
, then it would move exactly as in case 1 uniformly in the direction of the induction vector.
If a particle flew into a magnetic field with only one velocity component 
, then it would find itself in the same conditions as in case 2. And, therefore, it would move in a circle, the radius of which is again determined from Newton’s second law:
.
Thus, the resulting motion of the particle is simultaneously a uniform motion along the magnetic induction vector with a speed 
and uniform rotation in a plane perpendicular to the magnetic induction vector at a speed 
. The trajectory of such movement is a helical line or spiral (see Fig. 3.3). Spiral pitch 
– the distance traveled by the particle along the induction vector during one revolution:
.
How are the masses of the smallest charged particles (electron, proton, ions) known? How do you manage to “weigh” them (after all, you can’t put them on scales!)? Equation (3.5) shows that to determine the mass of a charged particle, you need to know the radius of its track when moving in a magnetic field. The radii of the tracks of the smallest charged particles are determined using a cloud chamber placed in a magnetic field, or using a more advanced bubble chamber. The principle of their operation is simple. In a cloud chamber, a particle moves in supersaturated water vapor and acts as a vapor condensation nucleus. Microdroplets that condense as a charged particle passes mark its trajectory. In a bubble chamber (invented only half a century ago by the American physicist D. Glaser), the particle moves in a superheated liquid, i.e. heated above its boiling point. This state is unstable and as the particle passes, boiling occurs and a chain of bubbles forms along its trail. A similar picture can be observed by throwing a grain of table salt into a glass of beer: as it falls, it leaves a trail of gas bubbles. Bubble chambers are the most important tools for recording the smallest charged particles, being, in fact, the main informative devices of experimental nuclear physics.
« Physics - 10th grade"
First, let's consider the simplest case, when electrically charged bodies are at rest.
The branch of electrodynamics devoted to the study of the equilibrium conditions of electrically charged bodies is called electrostatics.
What is an electric charge?
What charges are there?
With words electricity, electric charge, electric current you have met many times and managed to get used to them. But try to answer the question: “What is an electric charge?” The concept itself charge- this is a basic, primary concept that cannot be reduced at the current level of development of our knowledge to any simpler, elementary concepts.
Let us first try to find out what is meant by the statement: “This body or particle has an electric charge.”
All bodies are built from the smallest particles, which are indivisible into simpler ones and are therefore called elementary.
Elementary particles have mass and due to this they are attracted to each other according to the law of universal gravitation. As the distance between particles increases, the gravitational force decreases in inverse proportion to the square of this distance. Most elementary particles, although not all, also have the ability to interact with each other with a force that also decreases in inverse proportion to the square of the distance, but this force is many times greater than the force of gravity.
So in the hydrogen atom, shown schematically in Figure 14.1, the electron is attracted to the nucleus (proton) with a force 10 39 times greater than the force of gravitational attraction.
If particles interact with each other with forces that decrease with increasing distance in the same way as the forces of universal gravity, but exceed the gravitational forces many times, then these particles are said to have an electric charge. The particles themselves are called charged.
There are particles without an electric charge, but there is no electric charge without a particle.
The interaction of charged particles is called electromagnetic.
Electric charge determines the intensity of electromagnetic interactions, just as mass determines the intensity of gravitational interactions.
The electric charge of an elementary particle is not a special mechanism in the particle that could be removed from it, decomposed into its component parts and reassembled. The presence of an electric charge on an electron and other particles only means the existence of certain force interactions between them.
We, in essence, know nothing about charge if we do not know the laws of these interactions. Knowledge of the laws of interactions should be included in our ideas about charge. These laws are not simple, and it is impossible to outline them in a few words. Therefore, it is impossible to give a sufficiently satisfactory brief definition of the concept electric charge.
Two signs of electric charges.
All bodies have mass and therefore attract each other. Charged bodies can both attract and repel each other. This most important fact, familiar to you, means that in nature there are particles with electric charges of opposite signs; in the case of charges of the same sign, the particles repel, and in the case of different signs, they attract.
Charge of elementary particles - protons, which are part of all atomic nuclei, are called positive, and the charge electrons- negative. There are no internal differences between positive and negative charges. If the signs of the particle charges were reversed, then the nature of electromagnetic interactions would not change at all.
Elementary charge.
In addition to electrons and protons, there are several other types of charged elementary particles. But only electrons and protons can exist in a free state indefinitely. The rest of the charged particles live less than a millionth of a second. They are born during collisions of fast elementary particles and, having existed for an insignificantly short time, decay, turning into other particles. You will become familiar with these particles in 11th grade.
Particles that do not have an electrical charge include neutron. Its mass is only slightly greater than the mass of a proton. Neutrons, together with protons, are part of the atomic nucleus. If an elementary particle has a charge, then its value is strictly defined.
Charged bodies Electromagnetic forces in nature play a huge role due to the fact that all bodies contain electrically charged particles. The constituent parts of atoms - nuclei and electrons - have an electrical charge.
The direct action of electromagnetic forces between bodies is not detected, since the bodies in their normal state are electrically neutral.
An atom of any substance is neutral because the number of electrons in it is equal to the number of protons in the nucleus. Positively and negatively charged particles are connected to each other by electrical forces and form neutral systems.
A macroscopic body is electrically charged if it contains an excess amount of elementary particles with any one sign of charge. Thus, the negative charge of a body is due to the excess number of electrons compared to the number of protons, and the positive charge is due to the lack of electrons.
In order to obtain an electrically charged macroscopic body, that is, to electrify it, it is necessary to separate part of the negative charge from the positive charge associated with it or transfer a negative charge to a neutral body.
This can be done using friction. If you run a comb through dry hair, then a small part of the most mobile charged particles - electrons - will move from the hair to the comb and charge it negatively, and the hair will charge positively.
Equality of charges during electrification
With the help of experiment, it can be proven that when electrified by friction, both bodies acquire charges of opposite sign, but equal in magnitude.
Let's take an electrometer, on the rod of which there is a metal sphere with a hole, and two plates on long handles: one made of hard rubber and the other made of plexiglass. When rubbing against each other, the plates become electrified.
Let's bring one of the plates inside the sphere without touching its walls. If the plate is positively charged, then some of the electrons from the needle and rod of the electrometer will be attracted to the plate and collected on the inner surface of the sphere. At the same time, the arrow will be charged positively and will be pushed away from the electrometer rod (Fig. 14.2, a).
If you bring another plate inside the sphere, having first removed the first one, then the electrons of the sphere and the rod will be repelled from the plate and will accumulate in excess on the arrow. This will cause the arrow to deviate from the rod, and at the same angle as in the first experiment.
Having lowered both plates inside the sphere, we will not detect any deviation of the arrow at all (Fig. 14.2, b). This proves that the charges of the plates are equal in magnitude and opposite in sign.
Electrification of bodies and its manifestations. Significant electrification occurs during friction of synthetic fabrics. When you take off a shirt made of synthetic material in dry air, you can hear a characteristic crackling sound. Small sparks jump between the charged areas of the rubbing surfaces.
In printing houses, paper is electrified during printing and the sheets stick together. To prevent this from happening, special devices are used to drain the charge. However, the electrification of bodies in close contact is sometimes used, for example, in various electrocopying installations, etc.
Law of conservation of electric charge.
Experience with the electrification of plates proves that during electrification by friction, a redistribution of existing charges occurs between bodies that were previously neutral. A small portion of electrons moves from one body to another. In this case, new particles do not appear, and pre-existing ones do not disappear.
When bodies are electrified, law of conservation of electric charge. This law is valid for a system into which charged particles do not enter from the outside and from which they do not leave, i.e. for isolated system.
In an isolated system, the algebraic sum of the charges of all bodies is conserved.
q 1 + q 2 + q 3 + ... + q n = const. (14.1)
where q 1, q 2, etc. are the charges of individual charged bodies.
The law of conservation of charge has a deep meaning. If the number of charged elementary particles does not change, then the fulfillment of the charge conservation law is obvious. But elementary particles can transform into each other, be born and disappear, giving life to new particles.
However, in all cases, charged particles are born only in pairs with charges of the same magnitude and opposite in sign; Charged particles also disappear only in pairs, turning into neutral ones. And in all these cases, the algebraic sum of the charges remains the same.
The validity of the law of conservation of charge is confirmed by observations of a huge number of transformations of elementary particles. This law expresses one of the most fundamental properties of electric charge. The reason for the charge conservation is still unknown.
So far we have been studying a force that was not only Newtonian, but also almost identical in shape to the gravitational force. Therefore, the behavior of charged bodies under the influence of electric force should resemble the behavior of bodies under the influence of gravitational force; in other words, all the conclusions of Newtonian mechanics can be used to describe the behavior of charged bodies. To illustrate this point, and to get a sense of the orders of magnitude encountered in systems whose importance will be discovered later, consider a model of a planetary system of charged particles.
Let's imagine that a light, negatively charged particle, such as an electron, orbits a heavy, positively charged particle, such as a proton. The electron charge is negative and equal to st. Mass of an electron The charge of a proton is equal to the charge of an electron, but opposite in sign, and the mass of a proton is
Since the proton is approximately 1800 times heavier than the electron, we can assume that it is stationary and the electron revolves around it, just as we can assume that the Earth revolves around the stationary Sun 1] (Fig. 292).
Fig. 292. Planetary system of charged particles: an electron rotating in a circular orbit around a proton is acted upon by a Coulomb force directed radially to the center and equal in magnitude
The Coulomb force acts between an electron and a proton:
directed along the line connecting two particles.
Some idea of the magnitude of electrostatic forces can be obtained by comparing the electrical and gravitational forces acting between an electron and a proton. The difference is determined by the ratio of charge and mass (in other words, the ratio of electrical mass to gravitational mass); corresponding to these fundamental particles. The ratio of the magnitudes of gravitational and electromagnetic forces acting between an electron and a proton is
Thus, the gravitational force is approximately 1040 times weaker than the electrostatic force; it is in this sense that we say that the gravitational force is very, very weak.
It is quite surprising that the force we feel most strongly in the form of our own body weight is so weak on the scale of atomic sizes. Electrostatic forces, although they are responsible for the properties of substances and hold particles of a substance together, are almost completely shielded due to the fact that charged particles of different signs are presented in the same quantity. If the compensation were incomplete, say the difference would be one thousandth of a percent of particles on bodies of normal size, the corresponding electrostatic forces would significantly exceed gravitational ones.
The analysis of a planetary system of charged particles is carried out in the same way as the analysis of the solar system. From Newton's second law
and expressions for the acceleration of a body rotating at a constant speed in a circle,
But the force acting between positive and negative charges is
Mechanical energy of the system
Using (19.45), this expression can be written as
To obtain numerical values for various quantities, one must select the radius of the electron's orbit. Let us assume that the value
LABORATORY WORK No. 19.
Purpose of the work: study the tracks of charged particles using ready-made photographs.
Theory: Using a cloud chamber, tracks (traces) of moving charged particles are observed and photographed. The particle track is a chain of microscopic droplets of water or alcohol formed due to the condensation of supersaturated vapors of these liquids on ions. Ions are formed as a result of the interaction of a charged particle with atoms and molecules of vapors and gases located in the chamber.
Figure 1.
Let a particle with a charge Ze moves at speed V at a distance r from the electron of the atom (Fig. 1). Due to the Coulomb interaction with this particle, the electron receives some momentum in the direction perpendicular to the line of motion of the particle. The interaction of a particle and an electron is most effective when it passes along the trajectory segment closest to the electron and comparable to the distance r, for example equal to 2r. Then in the formula , where is the time during which the particle passes the trajectory segment 2r, i.e. ,a F- the average force of interaction between a particle and an electron during this time.
Strength F according to Coulomb's law, it is directly proportional to the charges of the particle ( Ze) and electron ( e) and is inversely proportional to the square of the distance between them. Therefore, the force of interaction between a particle and an electron is approximately equal to:
(approximately, since our calculations did not take into account the influence of the atomic nucleus of other electrons and atoms of the medium):
So, the momentum received by an electron is directly dependent on the charge of the particle passing near it and inversely dependent on its speed.
With some sufficiently large momentum, an electron is detached from an atom and the latter turns into an ion. For each unit of particle path, the more ions are formed
(and consequently, liquid droplets), the greater the charge of the particle and the lower its speed. This leads to the following conclusions that you need to know in order to be able to “read” a photograph of particle tracks:
1. Under other identical conditions, the track is thicker for the particle that has a larger charge. For example, at the same speeds, the track of particles is thicker than the track of a proton and an electron.
2. If the particles have the same charges, then the track is thicker for the one that has a lower speed and moves more slowly, hence it is obvious that by the end of the movement the track of the particle is thicker than at the beginning, since the speed of the particle decreases due to the loss of energy for the ionization of atoms of the medium.
3. By studying radiation at different distances from a radioactive substance, we found that ionizing and other effects - radiation stop abruptly at a certain distance characteristic of each radioactive substance. This distance is called mileage particles. Obviously, the range depends on the energy of the particle and the density of the medium. For example, in air at a temperature of 15 0 C and normal pressure, the range of a particle with an initial energy of 4.8 MeV is 3.3 cm, and the range of particles with an initial energy of 8.8 MeV is 8.5 cm. In a solid body. for example, in photographic emulsion, the range of particles with such energy is equal to several tens of micrometers.
If a cloud chamber is placed in a magnetic field, then the charged particles moving in it are acted upon by the Lorentz force, which is equal (for the case when the particle speed is perpendicular to the field lines):
Where Ze- particle charge, speed and IN - magnetic field induction. The left-hand rule allows us to show that the Lorentz force is always directed perpendicular to the particle velocity and, therefore, is a centripetal force:
Where T - the mass of the particle, r is the radius of curvature of its track. Hence (1).
If a particle has a speed much lower than the speed of light (i.e. the particle is not relativistic), then the relationship between kinetic energy and its radius of curvature has the form: 
(2)
From the obtained formulas, conclusions can be drawn that must also be used to analyze photographs of particle tracks.
1. The radius of curvature of the track depends on the mass, speed and charge of the particle. The smaller the radius (i.e., the deviation of the particle from rectilinear motion is greater), the lower the mass and speed of the particle and the greater its charge. For example, in the same magnetic field at the same initial velocities, the deflection of the electron will be greater than the deflection of the proton, and the photograph will show that the electron track is a circle with a smaller radius than the radius of the proton track. A fast electron will deflect less than a slow one. A helium atom that is missing an electron (ion Not +), the particles will deviate weaker, since at the same masses the charge of the particles is greater than the charge of a singly ionized helium atom. From the relationship between the energy of a particle and the radius of curvature of its track, it is clear that the deviation from rectilinear motion is greater in the case when the particle energy is less.
2. Since the speed of the particle decreases towards the end of its run, the radius of curvature of the track also decreases (the deviation from straight-line motion increases). By changing the radius of curvature, you can determine the direction of movement of the particle - the beginning of its movement where the curvature of the track is less.
3. Having measured the radius of curvature of the track and knowing some other quantities, we can calculate the ratio of its charge to mass for a particle:
This relationship serves as the most important characteristic of a particle and allows one to determine what kind of particle it is, or, as they say, to identify the particle, i.e. establish its identity (identification, similarity) to a known particle
If a decay reaction of an atomic nucleus has occurred in a cloud chamber, then from the tracks of particles - decay products, it is possible to determine which nucleus decayed. To do this, we need to remember that in nuclear reactions the laws of conservation of the total electric charge and the total number of nucleons are satisfied. For example, in react: 
the total charge of the particles entering the reaction is equal to 8 (8 + 0) and the charge of the reaction product particles is also equal to 8 (4 * 2 + 0). The total number of nucleons on the left is 17 (16+1) and on the right is also 17 (4 * 4+1). If it was not known which element’s nucleus decayed, then its charge can be calculated using simple arithmetic calculations, and then using the table of D.I. Mendeleev to find out the name of the element. The law of conservation of the total number of nucleons will make it possible to determine which isotope of this element the nucleus belongs to. For example, in react: 
Z = 4 – 1 = 3 and A = 8 – 1 = 7, therefore it is an isotope of lithium.
Devices and accessories: photographs of tracks, transparent paper, square, compass, pencil.
Work order:
The photograph (Fig. 2) shows the tracks of light element nuclei (the last 22 cm of their path). The nuclei moved in a magnetic field by induction IN= 2.17 Tesla, directed perpendicular to the photograph. The initial velocities of all nuclei are the same and perpendicular to the field lines.
Figure 2.
1. Study of tracks of charged particles (theoretical material).
1.1. Determine the direction of the magnetic field induction vector and make an explanatory drawing, taking into account that the direction of the speed of movement of particles is determined by the change in the radius of curvature of the track of a charged particle (the beginning of its movement is where the curvature of the track is less).
1.2. Explain why particle trajectories are circles using theory from the lab.
1.3. What is the reason for the difference in the curvature of the trajectories of different nuclei and why does the curvature of each trajectory change from the beginning to the end of the particle's path? Answer these questions using the theory for the laboratory work.
2. Studying tracks of charged particles using ready-made photographs (Fig. 2).
2.1. Place a sheet of transparent paper on the photo (you can use tracing paper) and carefully transfer track 1 and the right edge of the photo onto it.
2.2. Measure the radius of curvature R of the track of particle 1 approximately at the beginning and end of the run; for this you need to make the following constructions:
a) draw 2 different chords from the beginning of the track;
b) find the midpoint of chord 1 and then 2 using a compass and square;
c) then draw lines through the midpoints of the chord segments;) ;
c) the resulting number will be the serial number of the element;
d) using the periodic system of chemical elements, determine which element’s nucleus is particle III.
3. Draw a conclusion about the work done.
4. Answer security questions.
Security questions:
Which nucleus - deuterium or tritium - do tracks II and IV belong to (using photographs of tracks of charged particles and constructions accordingly for the answer)?
