point charge. Charge units. Coulomb's Law
In electrostatics, Coulomb's law is one of the fundamental ones. It is used in physics to determine the force of interaction between two fixed point charges or the distance between them. It is a fundamental law of nature that does not depend on any other laws. Then the shape of the real body does not affect the magnitude of the forces. In this article, we will tell plain language Coulomb's law and its application in practice.
Discovery history
Sh.O. Coulomb in 1785 for the first time experimentally proved the interactions described by the law. In his experiments, he used a special torsion balance. However, back in 1773, Cavendish proved, using the example of a spherical capacitor, that there is no electric field inside the sphere. This suggested that electrostatic forces change depending on the distance between the bodies. To be more precise - the square of the distance. Then his research was not published. Historically, this discovery was named after Coulomb, and the quantity in which the charge is measured has a similar name.
Wording
The definition of Coulomb's law is: in a vacuumF interaction of two charged bodies is directly proportional to the product of their modules and inversely proportional to the square of the distance between them.
It sounds short, but it may not be clear to everyone. In simple words: The more charge the bodies have and the closer they are to each other, the greater the force.
And vice versa: If you increase the distance between the charges - the force will become less.
The formula for Coulomb's rule looks like this:
Designation of letters: q - charge value, r - distance between them, k - coefficient, depends on the chosen system of units.
The value of the charge q can be conditionally positive or conditionally negative. This division is very conditional. When bodies come into contact, it can be transmitted from one to another. It follows that the same body can have a charge of different magnitude and sign. A point charge is such a charge or a body whose dimensions are much smaller than the distance of possible interaction.
It should be taken into account that the environment in which the charges are located affects the interaction F. Since it is almost equal in air and in vacuum, Coulomb's discovery is applicable only for these media, this is one of the conditions for applying this type of formula. As already mentioned, in the SI system, the unit of charge is Coulomb, abbreviated as Cl. It characterizes the amount of electricity per unit of time. It is a derivative of the basic SI units.
1 C = 1 A * 1 s
It should be noted that the dimension of 1 C is redundant. Due to the fact that the carriers repel each other, it is difficult to keep them in a small body, although the 1A current itself is small if it flows in a conductor. For example, in the same 100 W incandescent lamp, a current of 0.5 A flows, and in an electric heater and more than 10 A. Such a force (1 C) is approximately equal to the force acting on a body with a mass of 1 t from the side of the globe.
You may have noticed that the formula is almost the same as in the gravitational interaction, only if in Newtonian mechanics masses appear, then in electrostatics - charges.
Coulomb's formula for a dielectric medium
The coefficient, taking into account the values of the SI system, is determined in N 2 *m 2 /Cl 2. It is equal to:
In many textbooks, this coefficient can be found in the form of a fraction:
Here E 0 \u003d 8.85 * 10-12 C2 / N * m2 is an electrical constant. For a dielectric, E is added - the dielectric constant of the medium, then the Coulomb law can be used to calculate the forces of interaction of charges for vacuum and the medium.
Taking into account the influence of the dielectric, it has the form:
From here we see that the introduction of a dielectric between the bodies reduces the force F.
How are the forces directed?
Charges interact with each other depending on their polarity - the same charges repel, and the opposite (opposite) attract.
By the way, this is the main difference from a similar law of gravitational interaction, where bodies always attract. Forces directed along a line drawn between them is called the radius vector. In physics, it is denoted as r 12 and as a radius vector from the first to the second charge and vice versa. The forces are directed from the center of the charge to the opposite charge along this line if the charges are opposite, and in reverse side, if they are of the same name (two positive or two negative). In vector form:
The force applied to the first charge from the second is denoted as F 12. Then, in vector form, Coulomb's law looks like this:
To determine the force applied to the second charge, the designations F 21 and R 21 are used.
If the body has complex shape and it is large enough that at a given distance it cannot be considered a point, then it is divided into small sections and each section is considered as point charge. After the geometric addition of all the resulting vectors, the resulting force is obtained. Atoms and molecules interact with each other according to the same law.
Application in practice
Coulomb's works are very important in electrostatics; in practice, they are used in a number of inventions and devices. A striking example is the lightning rod. With its help, they protect buildings and electrical installations from thunderstorms, thereby preventing fire and equipment failure. When it rains with a thunderstorm, an induced charge of large magnitude appears on the earth, they are attracted towards the cloud. It turns out that a large electric field appears on the surface of the earth. Near the tip of the lightning rod, it has a large value, as a result of which a corona discharge is ignited from the tip (from the ground, through the lightning rod to the cloud). The charge from the ground is attracted to the opposite charge of the cloud, according to Coulomb's law. The air is ionized and tension electric field decreases near the end of the lightning rod. Thus, the charges do not accumulate on the building, in which case the probability of a lightning strike is small. If a blow to the building occurs, then through the lightning rod all the energy will go into the ground.
In serious scientific research use the greatest construction of the 21st century - the particle accelerator. In it, the electric field does the work of increasing the energy of the particle. Considering these processes from the point of view of the impact on a point charge by a group of charges, then all the relations of the law turn out to be valid.
Useful
The concept of electricity. Electrification. Conductors, semiconductors and dielectrics. Elementary charge and its properties. Coulomb's law. Electric field strength. The principle of superposition. Electric field as manifestations of interaction. Electric field of an elementary dipole.
The term electricity comes from the Greek word electron (amber).
Electrization is the process of imparting electrical energy to the body.
charge. This term was introduced in the 16th century by the English scientist and physician Gilbert.
ELECTRIC CHARGE IS A PHYSICAL SCALAR VALUE THAT CHARACTERIZES THE PROPERTIES OF BODIES OR PARTICLES TO ENTER AND ELECTROMAGNETIC INTERACTIONS AND DETERMINES THE FORCE AND ENERGY OF THESE INTERACTIONS.
Properties of electric charges:
1. In nature, there are two types of electric charges. Positive (appear on glass rubbed against skin) and negative (appear on ebonite rubbed against fur).
2. Charges of the same name repel, unlike charges attract.
3. Electric charge DOES NOT EXIST WITHOUT PARTICLES OF CHARGE CARRIERS (electron, proton, positron, etc.). For example, e / charge cannot be removed from an electron and other elementary charged particles.
4. Electric charge is discrete, i.e. the charge of any body is an integer multiple of elementary electric charge e(e = 1.6 10 -19 C). Electron (i.e.= 9,11 10 -31 kg) and proton (t p = 1.67 10 -27 kg) are respectively carriers of elementary negative and positive charges. (Particles with a fractional electric charge are known: – 1/3 e and 2/3 e - This quarks and antiquarks , but they were not found in the free state).
5. Electric charge - magnitude relativistically invariant , those. does not depend on the frame of reference, and therefore does not depend on whether this charge is moving or at rest.
6. From the generalization of experimental data, fundamental law of nature - charge conservation law: algebraic sum
ma electric charges of any closed system(systems that do not exchange charges with external bodies) remains unchanged, no matter what processes take place within this system.
The law was experimentally confirmed in 1843 by an English physicist
M. Faraday ( 1791-1867) and others, confirmed by the birth and annihilation of particles and antiparticles.
The unit of electric charge (derived unit, as it is determined through the unit of current strength) - pendant (C): 1 C - electric charge,
passing through the cross section of the conductor at a current strength of 1 A for a time of 1 s.
All bodies in nature are capable of being electrified; acquire an electrical charge. The electrification of bodies can be carried out different ways: contact (friction), electrostatic induction
etc. Any charging process is reduced to the separation of charges, in which an excess of a positive charge appears on one of the bodies (or part of the body), and an excess of a negative charge appears on the other (or other part of the body). Total charges of both signs contained in the bodies does not change: these charges are only redistributed between the bodies.
Electrification of bodies is possible because bodies consist of charged particles. In the process of electrification of bodies, electrons and ions that are in a free state can move. The protons remain in the nuclei.
Depending on the concentration of free charges, bodies are divided into conductors, dielectrics and semiconductors.
conductors- bodies in which the electric charge can be mixed throughout its volume. Conductors are divided into two groups:
1) conductors of the first kind (metals) - transfer to
of charges (free electrons) is not accompanied by chemical
transformations;
2) conductors of the second kind (for example, molten salts,
acid ranges) - the transfer of charges in them (positive and negative
ions) leads to chemical changes.
Dielectrics(for example, glass, plastics) - bodies in which there are practically no free charges.
Semiconductors (e.g. germanium, silicon) occupy
intermediate position between conductors and dielectrics. This division of bodies is very arbitrary, but the large difference in the concentrations of free charges in them causes huge qualitative differences in their behavior and therefore justifies the division of bodies into conductors, dielectrics and semiconductors.
ELECTROSTATICS- the science of fixed charges
Coulomb's law.
Law of interaction fixed point electric charges
Experimentally installed in 1785 by Sh. Coulomb using torsion balances.
similar to those used by G. Cavendish to determine the gravitational constant (this law was previously discovered by G. Cavendish, but his work remained unknown for more than 100 years).
point charge, is called a charged body or particle, the size of which can be neglected, compared with the distance to them.
Coulomb's law: the force of interaction between two fixed point charges located in a vacuum proportional to charges q 1 And q2, and is inversely proportional to the square of the distance r between them :
k - proportionality factor depending on the choice of system
in SI
Value ε 0 called electrical constant; it refers to
number fundamental physical constants and is equal to:
ε 0 = 8.85 ∙10 -12 C 2 / N∙m 2
In vector form, Coulomb's law in vacuum has the form:
where is the radius vector connecting the second charge with the first, F 12 is the force acting from the second charge on the first.
The accuracy of the implementation of the Coulomb law at large distances, up to
10 7 m, established during the study magnetic field with the help of satellites
in near-Earth space. The accuracy of its implementation at short distances, up to 10 -17 m, verified by experiments on the interaction of elementary particles.
Coulomb's law in the environment
In all media, the force of the Coulomb interaction is less than the force of interaction in vacuum or air. A physical quantity showing how many times the force of electrostatic interaction in vacuum is greater than in a given medium, is called the permittivity of the medium and is denoted by the letter ε.
ε = F in vacuum / F in medium
Coulomb's law general view in SI:
Properties of Coulomb forces.
1. Coulomb forces are forces of the central type, because directed along a straight line connecting the charges
The Coulomb force is an attractive force if the signs of the charges are different and a repulsive force if the signs of the charges are the same.
3. For Coulomb forces, Newton's 3rd law is valid
4. Coulomb forces obey the principle of independence or superposition, because the force of interaction between two point charges will not change when other charges appear near. The resulting force of electrostatic interaction acting on a given charge is equal to the vector sum of the forces of interaction of a given charge with each charge of the system separately.
F= F 12 + F 13 + F 14 + ∙∙∙ + F 1 N
Interactions between charges are carried out by means of an electric field. An electric field is a special form of the existence of matter, through which the interaction of electric charges is carried out. The electric field manifests itself by the fact that it acts with force on any other charge introduced into this field. An electrostatic field is created by stationary electric charges and propagates in space with a finite speed c.
Power characteristic electric field is called strength.
tension electric at some point is called a physical quantity equal to the ratio of the force with which the field acts on a positive test charge placed at a given point to the modulus of this charge.
The field strength of a point charge q:
Superposition principle: the strength of the electric field created by the system of charges at a given point in space is equal to the vector sum of the strengths of the electric fields created at this point by each charge separately (in the absence of other charges).
Coulomb's law quantitatively describes the interaction of charged bodies. It is a fundamental law, that is, established by experiment and does not follow from any other law of nature. It is formulated for immobile point charges in vacuum. In reality, point charges do not exist, but such charges can be considered, the dimensions of which are much smaller than the distance between them. The force of interaction in air is almost the same as the force of interaction in vacuum (it is weaker by less than one thousandth).
Electric charge is a physical quantity that characterizes the property of particles or bodies to enter into electromagnetic force interactions.
The law of interaction of fixed charges was first discovered by the French physicist C. Coulomb in 1785. Coulomb's experiments measured the interaction between balls whose dimensions are much smaller than the distance between them. Such charged bodies are called point charges.
Based on numerous experiments, Coulomb established the following law:
The force of interaction of two fixed point electric charges in vacuum is directly proportional to the product of their modules and inversely proportional to the square of the distance between them. It is directed along the straight line connecting the charges, and is an attractive force if the charges are opposite, and a repulsive force if the charges are of the same name.
If we designate charge modules as | q 1 | and | q 2 |, then Coulomb's law can be written in the following form:
\[ F = k \cdot \dfrac(\left|q_1 \right| \cdot \left|q_2 \right|)(r^2) \]
The coefficient of proportionality k in Coulomb's law depends on the choice of the system of units.
\[ k=\frac(1)(4\pi \varepsilon _0) \]
The full formula of Coulomb's law:
\[ F = \dfrac(\left|q_1 \right|\left|q_2 \right|)(4 \pi \varepsilon_0 \varepsilon r^2) \]
\(F\) - Coulomb Strength
\(q_1 q_2 \) - Electric charge of the body
\(r \) - Distance between charges
\(\varepsilon_0 = 8.85*10^(-12) \)- Electrical constant
\(\varepsilon \) - Dielectric constant of the medium
\(k = 9*10^9 \) - Coefficient of proportionality in Coulomb's law
Interaction forces obey Newton's third law: \(\vec(F)_(12)=\vec(F)_(21) \). They are repulsive forces with the same signs of charges and attractive forces with different signs.
Electric charge is usually denoted by the letters q or Q.
The totality of all known experimental facts allows us to draw the following conclusions:
There are two kinds of electric charges, conventionally called positive and negative.
Charges can be transferred (for example, by direct contact) from one body to another. Unlike body mass, electric charge is not an inherent characteristic of a given body. The same body in different conditions may have different charges.
Like charges repel, unlike charges attract. This also manifests itself fundamental difference electromagnetic forces from gravitational. Gravitational forces are always forces of attraction.
The interaction of fixed electric charges is called electrostatic or Coulomb interaction. The section of electrodynamics that studies the Coulomb interaction is called electrostatics.
Coulomb's law is valid for point charged bodies. In practice, Coulomb's law is well satisfied if the dimensions of the charged bodies are much smaller than the distance between them.
Note that in order for Coulomb's law to be fulfilled, 3 conditions are necessary:
- Point charges- that is, the distance between the charged bodies is much greater than their size.
- Immobility of charges. Otherwise, additional effects come into force: the magnetic field of the moving charge and the corresponding additional Lorentz force acting on another moving charge.
- Interaction of charges in vacuum.
IN international system The SI unit of charge is the pendant (C).
A pendant is a charge that passes in 1 s through the cross section of a conductor at a current strength of 1 A. The unit of current (ampere) in SI is, along with units of length, time and mass, the main unit of measurement.
Javascript is disabled in your browser.ActiveX controls must be enabled in order to make calculations!
Example 1
Task
A charged ball is brought into contact with exactly the same uncharged ball. Being at a distance \(r \u003d 15\) cm, the balls repel with a force\(F \u003d 1\) mN. What was the initial charge of the charged ball?
Solution
Upon contact, the charge will be divided exactly in half (the balls are the same). Based on this interaction force, we can determine the charges of the balls after contact (let's not forget that all quantities must be represented in SI units - \ (F \u003d 10 ^ (-3) \) H, \ ( r = 0.15 \) m):
\(F = \dfrac(k\cdot q^2)(r^2) , q^2 = \dfrac(F\cdot r^2)(k) \)
\(k=\dfrac(1)(4\cdot \pi \cdot \varepsilon _0) = 9\cdot 10^9 \)
\(q=\sqrt(\dfrac(f\cdot r^2)(k) ) = \sqrt(\dfrac(10^(-3)\cdot (0.15)^2 )(9\cdot 10^9) ) = 5\cdot 10^8 \)
Then, before the contact, the charge of the charged ball was twice as much: \(q_1=2\cdot 5\cdot 10^(-8)=10^(-7) \)
Answer
\(q_1=10^(-7)=10\cdot 10^(-6) \) C, or 10 µC.
Example 2
Task
Two identical small balls weighing 0.1 g each are suspended on non-conductive threads of length \(\displaystyle(\ell = 1\,(\text(m))) \) to one point. After the balls were given the same charges \(\displaystyle(q) \) , they dispersed a distance \(\displaystyle(r=9\,(\text(cm))) \). Air permittivity \(\displaystyle(\varepsilon=1)\). Determine the charges of the balls.
Data
\(\displaystyle(m=0,1\,(\text(r))=10^(-4)\,(\text(kg))) \)
\(\displaystyle(\ell=1\,(\text(m))) \)
\(\displaystyle(r=9\,(\text(cm))=9\cdot 10^(-2)\,(\text(m))) \)
\(\displaystyle(\varepsilon = 1) \)
\(\displaystyle(q) - ?\)
Solution
Since the balls are the same, the same forces act on each ball: the force of gravity \(\displaystyle(m \vec g) \), the force of the thread tension \(\displaystyle(\vec T) \) and the force of the Coulomb interaction (repulsion) \( \displaystyle(\vec F) \). The figure shows the forces acting on one of the balls. Since the ball is in equilibrium, the sum of all forces acting on it is 0. Also, the sum of the projections of the forces on the \(\displaystyle(OX) \) and \(\displaystyle(OY) \) axes is 0:
\(\begin(equation) ((\mbox(per axis )) (OX) : \atop ( \mbox( per axis )) (OY) : )\quad \left\(\begin(array)(ll) F-T \sin(\alpha) & =0 \\ T\cos(\alpha)-mg & =0 \end(array)\right.\quad(\text(or))\quad \left\(\begin(array )(ll) T\sin(\alpha) & =F \\ T\cos(\alpha) & = mg \end(array)\right. \end(equation) \)
Let's solve these equations together. Dividing the first equality term by term by the second, we get:
\(\begin(equation) (\mbox(tg)\,)= (F\over mg)\,. \end(equation) \)
Since the angle \(\displaystyle(\alpha) \) is small, then
\(\begin(equation) (\mbox(tg)\,)\approx\sin(\alpha)=(r\over 2\ell)\,. \end(equation) \)
Then the expression will take the form:
\(\begin(equation) (r\over 2\ell)=(F\over mg)\,. \end(equation) \)
The force \(\displaystyle(F) \) according to Coulomb's law is: \(\displaystyle(F=k(q^2\over\varepsilon r^2)) \). Substitute the value \(\displaystyle(F) \) into expression (52):
\(\begin(equation) (r\over 2\ell)=(kq^2\over\varepsilon r^2 mg)\, \end(equation) \)
whence we express the desired charge in general form:
\(\begin(equation) q=r\sqrt(r\varepsilon mg\over 2k\ell)\,. \end(equation) \)
After substituting the numerical values, we will have:
\(\begin(equation) q= 9\cdot 10^(-2)\sqrt(9\cdot 10^(-2)\cdot 1 \cdot 10^(-4)\cdot 9,8\over 2\ cdot 9\cdot 10^9\cdot 1)\, ((\text(Q)))=6.36\cdot 10^(-9)\, ((\text(Q)))\,.\end(equation )\)
It is proposed to independently check the dimension for the calculation formula.
Answer: \(\displaystyle(q=6,36\cdot 10^(-9)\,(\text(K))\,.) \)
Answer
\(\displaystyle(q=6,36\cdot 10^(-9)\,(\text(K))\,.) \)
Example 3
Task
What work must be done to move a point charge \(\displaystyle(q=6\,(\text(nCl))) \) from infinity to a point at a distance \(\displaystyle(\ell = 10\,(\ text(cm))) \) from the surface of a metal ball whose potential is \(\displaystyle(\varphi_(\text(w))=200\,(\text(B))) \), and whose radius is \(\displaystyle (R = 2\,(\text(cm))) \)? The balloon is in the air (count \(\displaystyle(\varepsilon=1) \)).
Data
\(\displaystyle(q=6\,(\text(nK))=6\cdot 10^(-9)\,(\text(K))) \)\(\displaystyle(\ell=10\, (\text(cm))) \)\(\displaystyle(\varphi_(\text(w))=200\,(\text(B))) \)\(\displaystyle(R=2\,(\ text(cm))) \) \(\displaystyle(\varepsilon = 1) \) \(\displaystyle(A) \) - ?
Solution
The work that needs to be done to transfer the charge from a point with potential \(\displaystyle(\varphi_1) \) to a point with potential \(\displaystyle(\varphi_2) \) is equal to the change in the potential energy of a point charge, taken with the opposite sign:
\(\begin(equation) A=-\Delta W_n\,. \end(equation) \)
It is known that \(\displaystyle(A=-q(\varphi_2-\varphi_1) ) \) or
\(\begin(equation) A=q(\varphi_1-\varphi_2) \,. \end(equation) \)
Since the point charge is initially at infinity, the potential at that point of the field is 0: \(\displaystyle(\varphi_1=0) \) .
Let's define the potential at the endpoint, i.e. \(\displaystyle(\varphi_2) \) .
Let \(\displaystyle(Q_(\text(w))) \) be the charge of the ball. By the condition of the problem, the potential of the ball is known (\(\displaystyle(\varphi_(\text(w))=200\,(\text(B))) \)) , then:
\(\begin(equation) \varphi_(\text(w))=(Q_(\text(w))\over 4\pi\varepsilon_o\varepsilon R)\, \end(equation) \)
\(\begin(equation) (\text(from))\quad Q_(\text(w))=\varphi_(\text(w))\cdot 4\pi\varepsilon_o\varepsilon R\,.\end( equation)\)
The value of the field potential at the end point, taking into account:
\(\begin(equation) \varphi_2=(Q_(\text(w))\over 4\pi\varepsilon_o\varepsilon(R+\ell) )= (\varphi_(\text(w))R\over (R+ \ell) )\,.\end(equation) \)
Substitute the value \(\displaystyle(\varphi_1) \) and \(\displaystyle(\varphi_2) \) into the expression, after which we get the required work:
\(\begin(equation) A=-q(\varphi_(\text(w))R\over (R+\ell) )\,.\end(equation) \)
As a result of calculations, we get: \(\displaystyle(A=-2\cdot 10^(-7)\,(\text(J))) \) .
Then the modulus of the interaction force between neighboring charges is equal to:
\(F = \dfrac(k\cdot q^2)(l^(2)_(1)) =\Delta l\cdot k_(pr) \)
Moreover, the lengthening of the cord is: \(\Delta l \u003d l\).
Whence the magnitude of the charge is equal to:
\(q=\sqrt(\frac(4\cdot l^3\cdot k_(pr))(k) ) \)
Answer
\(q=2\cdot l\cdot \sqrt(\frac(l\cdot k_(pr))(k) ) \)
In 1785, the French physicist Charles Coulomb experimentally established the basic law of electrostatics - the law of the interaction of two motionless point charged bodies or particles.
The law of interaction of motionless electric charges - Coulomb's law - the main (fundamental) physical law and can only be installed empirically. It does not follow from any other laws of nature.
If we designate charge modules as | q 1 | and | q 2 |, then Coulomb's law can be written in the following form:
\(~F = k \cdot \dfrac(|q_1| \cdot |q_2|)(r^2)\) , (1)
Where k– coefficient of proportionality, the value of which depends on the choice of units of electric charge. In the SI system \(~k = \dfrac(1)(4 \pi \cdot \varepsilon_0) = 9 \cdot 10^9\) N m 2 /Cl 2, where ε 0 is an electrical constant equal to 8.85 10 -12 C 2 /Nm 2 .
The wording of the law:
the force of interaction of two point motionless charged bodies in vacuum is directly proportional to the product of charge modules and inversely proportional to the square of the distance between them.
This force is called Coulomb.
Coulomb's law in this formulation is valid only for point charged bodies, because only for them the concept of distance between charges has a certain meaning. There are no point charged bodies in nature. But if the distance between the bodies is many times greater than their size, then neither the shape nor the size of the charged bodies, as experience shows, does not significantly affect the interaction between them. In this case, the bodies can be considered as point ones.
It is easy to find that two charged balls suspended on strings either attract each other or repel each other. It follows from this that the forces of interaction of two motionless point charged bodies are directed along the straight line connecting these bodies. Such forces are called central. If through \(~\vec F_(1,2)\) we denote the force acting on the first charge from the second, and through \(~\vec F_(2,1)\) the force acting on the second charge from the first (Fig. 1), then, according to Newton's third law, \(~\vec F_(1,2) = -\vec F_(2,1)\) . Denote by \(\vec r_(1,2)\) the radius vector drawn from the second charge to the first (Fig. 2), then
\(~\vec F_(1,2) = k \cdot \dfrac(q_1 \cdot q_2)(r^3_(1,2)) \cdot \vec r_(1,2)\) . (2)
If the charge signs q 1 and q 2 are the same, then the direction of the force \(~\vec F_(1,2)\) coincides with the direction of the vector \(~\vec r_(1,2)\) ; otherwise, the vectors \(~\vec F_(1,2)\) and \(~\vec r_(1,2)\) are directed in opposite directions.
Knowing the law of interaction of point charged bodies, it is possible to calculate the force of interaction of any charged bodies. To do this, the body must be mentally divided into such small elements that each of them can be considered a point. Adding geometrically the forces of interaction of all these elements with each other, it is possible to calculate the resulting force of interaction.
The discovery of Coulomb's law is the first concrete step in the study of the properties of electric charge. The presence of an electric charge in bodies or elementary particles means that they interact with each other according to the Coulomb law. No deviations from the strict implementation of Coulomb's law have been found at present.
Coulomb experience
The need for Coulomb's experiments was caused by the fact that in the middle of the 18th century. accumulated a lot of qualitative data on electrical phenomena. There was a need to give them a quantitative interpretation. Since the forces of electrical interaction were relatively small, a serious problem arose in creating a method that would make it possible to make measurements and obtain the necessary quantitative material.
The French engineer and scientist C. Coulomb proposed a method for measuring small forces, which was based on the following experimental fact, discovered by the scientist himself: the force arising from the elastic deformation of a metal wire is directly proportional to the angle of twist, the fourth power of the wire diameter and inversely proportional to its length:
\(~F_(ynp) = k \cdot \dfrac(d^4)(l) \cdot \varphi\) ,
Where d– diameter, l- wire length, φ - twist angle. In the above mathematical expression, the proportionality coefficient k was found empirically and depended on the nature of the material from which the wire was made.
This pattern was used in the so-called torsion balances. The created scales made it possible to measure negligible forces of the order of 5 10 -8 N.
Rice. 3The torsion balance (Fig. 3, a) consisted of a light glass beam 9 10.83 cm long, suspended from a silver wire 5 about 75 cm long, 0.22 cm in diameter. At one end of the rocker was a gilded elderberry ball 8 , and on the other - a counterweight 6 - a paper circle dipped in turpentine. The upper end of the wire was attached to the instrument head 1 . There was also a pointer here. 2 , with the help of which the angle of twisting of the thread was counted on a circular scale 3 . The scale has been graduated. The whole system was housed in glass cylinders. 4 And 11 . In the upper cover of the lower cylinder there was a hole into which a glass rod with a ball was inserted. 7 at the end. In the experiments, balls with diameters ranging from 0.45 to 0.68 cm were used.
Before the start of the experiment, the head indicator was set to zero. Then the ball 7 charged from a pre-electrified ball 12 . When the ball touches 7 with moving ball 8 charge was redistributed. However, due to the fact that the diameters of the balls were the same, the charges on the balls were the same. 7 And 8 .
Due to the electrostatic repulsion of the balls (Fig. 3, b), the rocker 9 turned to some angle γ (on a scale 10 ). With head 1 this rocker returned to its original position. On a scale 3 pointer 2 allowed to determine the angle α thread twisting. Total twist angle φ = γ + α . The force of the interaction of the balls was proportional φ , i.e., the angle of twist can be used to judge the magnitude of this force.
At a constant distance between the balls (it was fixed on a scale 10 in degree measure) the dependence of the force of electrical interaction of point bodies on the magnitude of the charge on them was studied.
To determine the dependence of force on the charge of the balls, Coulomb found a simple and ingenious way to change the charge of one of the balls. To do this, he connected a charged ball (balls 7 or 8 ) with the same size uncharged (ball 12 on the insulating handle). In this case, the charge was distributed equally between the balls, which reduced the investigated charge by 2, 4, etc. times. The new value of the force at the new value of the charge was again determined experimentally. At the same time, it turned out that the force is directly proportional to the product of the charges of the balls:
\(~F \sim q_1 \cdot q_2\) .
The dependence of the electrical interaction force on the distance was discovered as follows. After the charge was communicated to the balls (they had the same charge), the rocker was deviated by a certain angle γ . Then turning the head 1 this angle is reduced to γ 1 . Total angle of twist φ 1 = α 1 + (γ - γ 1)(α 1 - head rotation angle). When the angular distance of the balls decreases to γ 2 total twist angle φ 2 = α 2 + (γ - γ 2). It was noticed that if γ 1 = 2γ 2 , THEN φ 2 = 4φ 1 , i.e., when the distance decreased by a factor of 2, the interaction force increased by a factor of 4. The moment of force increased by the same amount, since during torsion deformation the moment of force is directly proportional to the angle of twist, and hence the force (the arm of the force remained unchanged). From this follows the conclusion: The force between two charged spheres is inversely proportional to the square of the distance between them:
\(~F \sim \dfrac(1)(r^2)\) .
Literature
- Myakishev G.Ya. Physics: Electrodynamics. 10-11 cells: textbook. For in-depth study physics / G.Ya. Myakishev, A.Z. Sinyakov, B.A. Slobodskov. – M.: Bustard, 2005. – 476 p.
- Volshtein S. L. et al. Methods physical science at school: A guide for the teacher / S.L. Volshtein, S.V. Pozoisky, V.V. Usanov; Ed. S.L. Volshtein. - Mn.: Nar. asveta, 1988. - 144 p.
Most frequently asked questions
Is it possible to make a seal on a document according to the provided sample? Answer Yes, it's possible. Submit to our email address scanned copy or photo good quality and we will make the necessary duplicate.
What types of payment do you accept?
Answer You can pay for the document at the time of receipt by the courier, after you check the correctness of filling and the quality of the diploma. This can also be done at the office of postal companies offering cash on delivery services.
All terms of delivery and payment of documents are described in the section "Payment and Delivery". We are also ready to listen to your suggestions on the terms of delivery and payment for the document.
Can I be sure that after placing an order you will not disappear with my money? Answer We have quite a long experience in the field of diploma production. We have several sites that are constantly updated. Our specialists work in different corners countries, producing over 10 documents a day. Over the years, our documents have helped many people solve employment problems or move to higher paying jobs. We have earned trust and recognition among customers, so there is absolutely no reason for us to do this. Moreover, it is simply impossible to do it physically: you pay for your order at the time of receiving it in your hands, there is no prepayment.
Can I order a diploma from any university? Answer In general, yes. We have been working in this area for almost 12 years. During this time, an almost complete database of documents issued by almost all universities in the country and abroad has been formed. different years issuance. All you need is to choose a university, specialty, document, and fill out an order form.
What should I do if I find typos and errors in a document?
Answer When receiving a document from our courier or postal company, we recommend that you carefully check all the details. If a typo, error or inaccuracy is found, you have the right not to take the diploma, and you must indicate the shortcomings found personally to the courier or in writing by sending an e-mail.
As soon as possible, we will correct the document and resend it to the specified address. Of course, the shipping will be paid by our company.
To avoid such misunderstandings, before filling out the original form, we send a layout of the future document to the customer's mail for verification and approval of the final version. Before sending the document by courier or mail, we also take an additional photo and video (including in ultraviolet light) so that you have visual representation about what you will end up with.
What do you need to do to order a diploma from your company?
Answer To order a document (certificate, diploma, academic certificate, etc.), you must fill out an online order form on our website or provide your e-mail so that we send you a questionnaire form, which you need to fill out and send back to us.
If you do not know what to indicate in any field of the order form/questionnaire, leave them blank. Therefore, we will clarify all the missing information over the phone.
Latest reviews
Valentine:
You saved our son from being fired! The fact is that after dropping out of school, the son went into the army. And when he returned, he did not want to recover. Worked without a degree. But recently they began to fire everyone who does not have a “crust. Therefore, we decided to contact you and did not regret it! Now he works calmly and is not afraid of anything! Thank you!
Search
We may notify you of new articles,