FORCE FIELD

FORCE FIELD

A part of space (limited or unlimited), at each point a material object placed there is affected by , the magnitude and direction of which depend either only on the coordinates x, y, z of this point, or on the coordinates and time t. In the first case, S., called. stationary, and in the second - non-stationary. If the force at all points of a linear path has the same value, that is, does not depend on the coordinates, then the force is called. homogeneous.

SP, in which the field forces acting on a material object moving in it, depends only on the initial and final position of the object and does not depend on the type of its trajectory, called. potential. This work can be expressed in terms of the potential energy of the particle P (x, y, z):

A=П(x1, y1, z1)-П(x2, y2, z2),

where x1, y1, z1 and x2, y2, z2 are the coordinates of the initial and final positions of the particle, respectively. When a particle moves in a potential space under the influence of only field forces, the law of mechanical conservation takes place. energy, making it possible to establish a relationship between the speed of a particle and its position in the center of space.

Physical encyclopedic Dictionary. - M.: Soviet Encyclopedia. . 1983 .

FORCE FIELD

A part of space (limited or unlimited), at each point a material particle placed there is acted upon by a force of a certain numerical value and direction, depending only on the coordinates x, y, z this point.

This S. p. is called. stationary; if the field strength also depends on time, then S. p. is called. non-stationary; if the force at all points of a s.p. has the same value, i.e., does not depend on coordinates or time, the s.p. is called. homogeneous.

Stationary S. p. can be specified by equations Where F x , F y , F z -

field strength projections F. If such a function exists U(x, y,

z), called the force function, U(x,y, z), and the force F can be defined through this function by the equalities: or

. The condition for the existence of a power function for a given S. item is that or . When moving in a potential S. point from a point M 1 (x 1 ,y 1 ,z 1 )exactly M 2 (x 2, y 2,

z 2) the work of the field forces is determined by equality and does not depend on the type of trajectory along which the point of application of the force moves. If such a function exists Surfaces z) = const, for which the function maintains a constant state. Examples of potential static fields: a uniform gravitational field, for which U= -mgz, Where T - the mass of a particle moving in the field, g- acceleration of gravity (axis directed vertically upward); Newtonian flight of gravity, for which U = km/r, where r = - distance from the center of gravity, k - constant coefficient for a given field. potential energy P associated with U addiction P(x,)= = - If such a function exists z). Study of particle motion in potential. item (in the absence of other forces) is significantly simplified, since in this case the law of conservation of mechanics takes place. energy, which makes it possible to establish a direct relationship between the speed of a particle and its position in the solar system. With. POWER LINES- a family of curves characterizing the spatial distribution of the vector field of forces; the direction of the field vector at each point coincides with the tangent to the line. Thus, level of S. l. arbitrary vector field A (x, y, z) are written in the form:

Density S. l. characterizes the intensity (magnitude) of the force field. Concept of S. l. introduced by M. Faraday during the study of magnetism, and then further developed in the works of J. C. Maxwell on electromagnetism. Maxwell tension tensor el.-magn. fields.

Along with the use of the concept of S. l. more often they simply talk about field lines: electrical intensity. fields E, magnetic induction fields IN etc.

Physical encyclopedia. In 5 volumes. - M.: Soviet Encyclopedia. Chief Editor A. M. Prokhorov. 1988 .

See what a “FORM FIELD” is in other dictionaries:

Force field is a polysemantic term used in the following meanings: Force field (physics) vector field of forces in physics; A force field (science fiction) is some kind of invisible barrier, the main function of which is to protect some ... Wikipedia

A part of space, at each point of which a force of a certain magnitude and direction acts on a particle placed there, depending on the coordinates of this point, and sometimes on time. In the first case, the force field is called stationary, and in... ... Big Encyclopedic Dictionary

force field- An area of ​​space in which, when placed there, material point there is a force that depends on the coordinates of this point in the reference system under consideration and on time. [Collection of recommended terms. Issue 102. Theoretical mechanics. Academy... ... Technical Translator's Guide

A part of space, at each point of which a force of a certain magnitude and direction acts on a particle placed there, depending on the coordinates of this point, and sometimes on time. In the first case, the force field is called stationary, and in... ... encyclopedic Dictionary

force field- jėgų laukas statusas T sritis Standartizacija ir metrologija apibrėžtis Vektorinis laukas, kurio bet kuriame taške esančią dalelę veikia tik nuo taško padėties priklausančios jėgos (nuostovusis jėgų laukas) nuo taško padėties ir laiko… … Penkiakalbis aiškinamasis metrologijos terminų žodynas

force field- jėgų laukas statusas T sritis fizika atitikmenys: engl. force field vok. Kraftfeld, n rus. force field, n; force field, n pranc. champ de forces, m … Fizikos terminų žodynas

FORCE FIELD- In physics, this term can be given precise definition, in psychology it is used typically metaphorically and usually refers to any or all influences on behavior. It is usually used quite holistically - a force field... ... Dictionary in psychology

A part of space (limited or unlimited), at each point of which a force of a certain magnitude and direction acts on a material particle placed there, depending either only on the x, y, z coordinates of this point, or on... ... Great Soviet Encyclopedia

A part of space, at each point, a force of a certain magnitude and direction acts on a particle placed there, depending on the coordinates of this point, and sometimes on time. In the first case, S. p. is called. stationary, and in the second... ... Natural science. encyclopedic Dictionary

force field- A region of space in which a material point placed there is acted upon by a force that depends on the coordinates of this point in the reference system under consideration and on time... Polytechnic terminological explanatory dictionary

Force field is a physical space that satisfies the condition that the points of a mechanical system located in this space are acted upon by forces that depend on the position of these points or on the position of the points and time (but not on their velocities).

Force field, whose forces do not depend on time is called stationary(examples of a force field are the gravity field, the electrostatic field, the elastic force field).

Potential force field.

Stationary force field called potential, if the work of field forces acting on a mechanical system does not depend on the shape of the trajectories of its points and is determined only by their initial and final positions. These forces are called potential forces or conservative forces.

Let us prove that the above condition is satisfied if there is a unique coordinate function:

called the field force function, the partial derivatives of which with respect to the coordinates of any point M i (i=1, 2...n) are equal to the projection tions of the force applied to this point on the corresponding axes, i.e.

The elementary work of force applied to each point can be determined by the formula:

The elementary work of forces applied to all points of the system is equal to:

Using the formulas we get:

As can be seen from this formula, the elementary work of the potential field forces is equal to the total differential of the force function. The work of the field forces on the final displacement of the mechanical system is equal to:

that is, the work of forces acting on the points of a mechanical system in a potential field is equal to the difference in the values ​​of the force function in the final and initial positions of the system and does not depend on the shape of the trajectories of the points of this system. positions of the system and does not depend on the shape of the trajectories of the points of this system. It follows from this that the force field for which the force function exists is indeed potential.

In space, at each point of which a force of a certain magnitude and direction (force vector) acts on a test particle.

Technically distinguished (as is done for other types of fields)

• stationary fields, the magnitude and direction of which can depend solely on a point in space (coordinates x, y, z), and
• non-stationary force fields, also depending on the moment of time t.

• a uniform force field for which the force acting on the test particle is the same at all points in space and
• a non-uniform force field that does not have this property.

The simplest to study is a stationary homogeneous force field, but it also represents the least general case.

Potential fields

If the work of the field forces acting on a test particle moving in it does not depend on the trajectory of the particle, and is determined only by its initial and final positions, then such a field is called potential. For it, we can introduce the concept of potential energy of a particle - a certain function of particle coordinates such that the difference in its values ​​at points 1 and 2 is equal to the work done by the field when moving a particle from point 1 to point 2.

The force in a potential field is expressed in terms of potential energy as its gradient:

Examples of potential force fields:

Literature

E. P. Razbitnaya, V. S. Zakharov “Course of Theoretical Physics”, book 1. - Vladimir, 1998.

Wikimedia Foundation.

2010.

Force field is a polysemantic term used in the following meanings: Force field (physics) vector field of forces in physics; A force field (science fiction) is some kind of invisible barrier, the main function of which is to protect some ... Wikipedia

See what “Force field (physics)” is in other dictionaries:

Field is a polysemantic concept associated with extension in space: field in Wiktionary ... Wikipedia

- (from ancient Greek physis nature). The ancients called physics any study of the surrounding world and natural phenomena. This understanding of the term physics remained until the end of the 17th century. Later, a number of special disciplines appeared: chemistry, which studies the properties... ... Collier's Encyclopedia

A force field acting on moving electric charges and on bodies possessing a magnetic moment (See Magnetic moment), regardless of their state of motion. The magnetic field is characterized by the magnetic induction vector B, which determines: ... ... Great Soviet Encyclopedia

The concept of “field” is encountered very often in physics. From a formal point of view, the definition of a field can be formulated as follows: if at each point in space the value of a certain quantity, scalar or vector, is given, then they say that a scalar or vector field of this quantity is given, respectively .

More specifically, it can be stated that if a particle at every point in space is exposed to the influence of other bodies, then it is in a field of forces or force field .

The force field is called central, if the direction of the force at any point passes through some fixed center, and the magnitude of the force depends only on the distance to this center.

The force field is called homogeneous, if at all points of the field strength, acting on the particle, identical in magnitude and direction.

Stationary called time-invariant field.

If the field is stationary, then it is possible that Job field strength over some particle does not depend on the shape of the path , along which the particle moved and is completely determined by specifying the initial and final positions of the particle . Field strengths having this property are called conservative. (Not to be confused with the political orientation of parties...)

The most important property conservative forces is that their work on arbitrary closed path is zero. Indeed, a closed path can always be arbitrarily divided by two points into some two sections - section I and section II. When moving along the first section in one direction, work is done . When moving along the same section in the opposite direction, work is done – in the formula for work (3.7), each displacement element is replaced by the opposite sign: . Therefore, the integral as a whole changes sign to the opposite.

Then work on a closed path

Since, by definition of conservative forces, their work does not depend on the shape of the trajectory, then . Hence

The converse is also true: if the work on a closed path is zero, then the field forces are conservative . Both features can be used to determine conservative forces.

The work done by gravity near the Earth's surface is found by the formula A=mg(h 1 -h 2) and obviously does not depend on the shape of the path. Therefore, gravity can be considered conservative. This is a consequence of the fact that the gravity field within the laboratory can be considered homogeneous with very high accuracy. Has the same property any uniform stationary field, which means the forces of such a field are conservative. As an example, we can recall the electrostatic field in a flat capacitor, which is also a field of conservative forces.

Central field forces Also conservative. Indeed, their work on displacement is calculated as

In addition to contact interactions that occur between bodies in contact, interactions between bodies distant from each other are also observed. For example, the interaction between the Sun and the Earth, the Earth and the Moon, the Earth and a body raised above its surface, the interaction between electrified bodies. Such interactions are carried out through physical fields, which are a special form of matter. Each body creates a special state in the space surrounding it, called forceful field. This field manifests itself in the action of forces on other bodies. For example, the Earth creates a gravitational field. In it, every body of mass m at every point near the Earth’s surface is acted upon by a force - mg.

Forces whose work does not depend on the path along which the particle moved, but is determined only by the initial and final position of the particle, are called conservative.

Let us show that the work of conservative forces on any closed path is equal to zero.

Consider an arbitrary closed path. Let's divide it with randomly selected points 1 and 2 into two sections: I and II. Work on a closed path is equal to:

Fig. 18.1. Work of conservative forces on a closed path

Changing the direction of movement along section II to the opposite is accompanied by the replacement of all elementary displacements dr by (-dr), which causes the sign to be reversed. Then:

Now, substituting (18.2.) into (18.1.), we find that A = 0, i.e. We have proven the above statement. Another definition of conservative forces can be formulated as follows: conservative forces, these are forces whose work on any closed path is zero.

All forces that are not conservative are called non-conservative. Non-conservative forces include friction and resistance forces.

If the forces acting on a particle at all points of the field are identical in magnitude and direction, then the field is called homogeneous.

A field that does not change over time is called stationary. In the case of a uniform stationary field: F=const.

Statement: the forces acting on a particle in a uniform stationary field are conservative.

Let's prove this statement. Since the field is homogeneous and stationary, then F=const. Let's take two arbitrary points 1 and 2 in this field (Fig. 18.2.) and calculate the work done on the particle when it moves from point 1 to point 2.

18.2. Work of forces in a uniform stationary field on the way from point 1 to point 2

The work done by forces acting on a particle in a uniform stationary field is equal to:

where r F is the projection of the displacement vector r 12 onto the direction of the force, r F is determined only by the positions of points 1 and 2, and does not depend on the shape of the trajectory. Then, the work of force in this field does not depend on the shape of the path, but is determined only by the positions of the initial and final points of movement, i.e. the forces of a uniform stationary field are conservative.

Near the Earth's surface, the gravity field is a uniform stationary field and the work done by the force mg is equal to:

where (h 1 -h 2) is the projection of displacement r 12 on the direction of force, force mg is directed vertically downward, gravity is conservative.

Forces that depend only on the distance between interacting particles and are directed along a straight line passing through these particles are called central. Examples of central forces are: Coulomb, gravitational, elastic.