Find the work of the field forces on the displacement of the charge. Work in an electric field

If in the electrostatic field of a point charge q another point charge moves from point 1 to point 2 along an arbitrary trajectory q0, then the force applied to the charge does work. Force work on elementary displacement d l is equal to

Work while moving the charge q0 from point 1 to point 2

Work A 12 does not depend on the trajectory of movement, and determined only by the positions of the start and end points. Therefore, the electrostatic field of a point charge is potential , and the electrostatic forces conservative .

Thus, the work of moving a charge in an electrostatic field along any closed loop L zero

The integral is called the circulation of the tension vector. From its vanishing it follows that l The lines of the electrostatic field can never be closed on themselves. They start and end on charges, or go to infinity. This indicates the presence in nature of two kinds of electric charges. Formula valid only for an electrostatic field.

When moving charges, their relative position changes, so the work done by electric forces in this case is equal to the change in the potential energy of the charge being moved:

Potential charge energy q0 located in the charge field q on distance r from it is equal to

Assuming that when the charge is removed to infinity, the potential energy vanishes, we get: const = 0.

For namesake charges potential energy of their interaction (repulsion)positive, for dissimilar charges potential energy from the interaction (attraction)negative.

Anywhere in the field the potential energy W of the charge is numerically equal to the work that must be done to move the charge from infinity to this point.

The ratio depends on q and r. This value is called the potential:

Unit of electrical potential - volt(AT).

It characterizes the potential energy that a positive unit charge would have if placed at a given point in the field. For the field of a point charge: .The potential of a given point of the field is equal to the work of moving a unit positive charge from a given point to infinity.

The potential of the field created by a system of point charges is equal to the algebraic sum of the potentials of all these charges: .

The work of the field forces when moving the charge q' from point 1 to point 2 can be written as:

the value called potential difference (voltage) of the electric field.

What is tension really? It is a way of describing and measuring the strength of an electric field. Voltage itself cannot exist without an electronic field around positive and negative charges. Just like the magnetic field surrounds the North and South Poles.

According to modern concepts, electrons do not have mutual influence. An electric field is something that comes from one charge and its presence can be felt by another.

The same can be said about the concept of tension! It just helps us imagine what an electric field might look like. To be honest, it has no shape, no size, nothing of the sort. But the field functions with a certain force on the electrons.

Forces and their action on a charged particle

A charged electron is subjected to a force with some acceleration, causing it to move faster and faster. This force does work to move the electron.

Field lines are imaginary outlines that appear around charges (determined by the electric field), and if we place any charge in this area, it will experience a force.

Field line properties:

• travel from north to south;
• do not have mutual intersections.

Why don't two lines of force intersect? Because it doesn't happen in real life. What is being said is a physical model and nothing more. Physicists invented it to describe the behavior and characteristics of an electric field. The model is very good at this. But remembering that this is just a model, we need to know what such lines are for.

The lines of force show:

• directions of electric fields;
• tension. The closer the lines, the greater the field strength and vice versa.

If the drawn lines of force of our model intersect, the distance between them will become infinitely small. Because of the strength of the field as a form of energy, and because of the fundamental laws of physics, this is not possible.

What is potential?

Potential is the energy that is spent on the movement of a charged particle from the first point, which has zero potential, to the second point.

The potential difference between points A and B is the work done by forces to move a certain positive electron along an arbitrary trajectory from A to B.

The greater the potential of an electron, the greater the flux density per unit area. This phenomenon is similar to gravity. The greater the mass, the greater the potential, the more intense and dense the gravitational field per unit area.

A small low potential charge with a thinned flux density is shown in the following figure.

And below is a charge with a large potential and flux density.

For example: during a thunderstorm, electrons are depleted at one point and collected at another, forming an electric field. When the force becomes sufficient to break the permittivity, a lightning strike (consisting of electrons) is produced. When equalizing the potential difference, the electric field is destroyed.

electrostatic field

This is a kind of electric field, unchanging over time, formed by charges that do not move. The work of moving an electron is determined by the relations,

where r1 and r2 are the distances of the charge q to the initial and final points of the motion trajectory. According to the formula obtained, it can be seen that the work when moving a charge from point to point does not depend on the trajectory, but depends only on the beginning and end of the movement.

A force acts on each electron, and therefore, when an electron moves in a field, a certain work is performed.

In an electrostatic field, the work depends only on the final destinations, and not on the trajectory. Therefore, when the movement occurs in a closed loop, the charge comes to its original position, and the amount of work becomes equal to zero. This is because the potential drop is zero (because the electron returns to the same point). Since the potential difference is zero, the net work will also be zero, because the fall potential is equal to the work divided by the value of the charge, expressed in coulombs.

On a uniform electric field

A homogeneous electric field is called between two oppositely charged flat metal plates, where the lines of tension are parallel to each other.

Why is the force acting on a charge in such a field always the same? Thanks to symmetry. When the system is symmetrical and there is only one measurement variation, all dependence disappears. There are many other fundamental reasons for the answer, but the symmetry factor is the simplest.

The work of moving a positive charge

Electric field is the flow of electrons from "+" to "-", leading to a high intensity of the region.

Flow is the number of electric field lines passing through it. In which direction will the positive electrons move? Answer: in the direction of the electric field from positive (high potential) to negative (low potential). Therefore, a positively charged particle will move in this direction.

The intensity of the field at any point is defined as the force acting on a positive charge placed at that point.

The work consists in the transfer of electron particles along the conductor. According to Ohm's law, you can determine the work with different variations of the formulas in order to carry out the calculation.

From the law of conservation of energy it follows that work is a change in energy in a separate segment of the chain. Moving a positive charge against an electric field requires work, and the result is a gain in potential energy.

Conclusion

From the school curriculum, we remember that an electric field is formed around charged particles. Any charge in an electric field is affected by a force, and as a result, some work is done when the charge moves. A larger charge creates a larger potential, which produces a more intense or stronger electric field. This means that there is more flow and density per unit area.

The important point is that work must be done by a certain force to move the charge from a high potential to a low one. This reduces the charge difference between the poles. Moving electrons from a current to a point requires energy.

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ELECTRIC CHARGE. ELEMENTARY PARTICLES.

Electric charge q - physical quantity that determines the intensity of electromagnetic interaction.

[q] = l Cl (Coulomb).

Atoms are made up of nuclei and electrons. The nucleus contains positively charged protons and uncharged neutrons. Electrons carry a negative charge. The number of electrons in an atom is equal to the number of protons in the nucleus, so the atom as a whole is neutral.

The charge of any body: q = ±Ne, where e \u003d 1.6 * 10 -19 C is the elementary or minimum possible charge (electron charge), N- the number of excess or missing electrons. In a closed system, the algebraic sum of the charges remains constant:

q 1 + q 2 + … + q n = const.

A point electric charge is a charged body whose dimensions are many times smaller than the distance to another electrified body interacting with it.

Coulomb's Law

Two fixed point electric charges in vacuum interact with forces directed along a straight line connecting these charges; the modules of these forces are directly proportional to the product of the charges and inversely proportional to the square of the distance between them:

Proportionality factor

where is the electric constant.

where 12 is the force acting from the second charge to the first, and 21 - from the first to the second.

ELECTRIC FIELD. TENSION

The fact of the interaction of electric charges at a distance can be explained by the presence of an electric field around them - a material object, continuous in space and capable of acting on other charges.

The field of motionless electric charges is called electrostatic.

The characteristic of the field is its strength.

Electric field strength at a given point is a vector whose modulus is equal to the ratio of the force acting on a point positive charge to the magnitude of this charge, and the direction coincides with the direction of the force.

Field strength of a point charge Q on distance r from it is equal to

Principle of superposition of fields

The field strength of the system of charges is equal to the vector sum of the field strengths of each of the charges of the system:

The dielectric constant medium is equal to the ratio of field strengths in vacuum and in matter:

It shows how many times the substance weakens the field. Coulomb's law for two point charges q and Q located at a distance r in a medium with a permittivity:

Field strength at a distance r from charge Q is equal to

POTENTIAL ENERGY OF A CHARGED BODY IN A HOMOGENEOUS ELECTRIC STATIC FIELD

Between two large plates, charged with opposite signs and located in parallel, we place a point charge q.

Since the electric field between the plates with intensity is uniform, then the force acts on the charge at all points F = qE, which, when a charge moves a distance along, does work

This work does not depend on the shape of the trajectory, that is, when moving the charge q along an arbitrary line L work will be the same.

The work of an electrostatic field in moving a charge does not depend on the shape of the trajectory, but is determined exclusively by the initial and final states of the system. It, as in the case of the gravity field, is equal to the change in potential energy, taken with the opposite sign:

From a comparison with the previous formula, it can be seen that the potential energy of a charge in a uniform electrostatic field is:

Potential energy depends on the choice of the zero level and therefore has no deep meaning by itself.

ELECTROSTATIC FIELD POTENTIAL AND VOLTAGE

Potential a field is called, the work of which, when moving from one point of the field to another, does not depend on the shape of the trajectory. Potential are the gravity field and the electrostatic field.

The work done by the potential field is equal to the change in the potential energy of the system, taken with the opposite sign:

Potential- the ratio of the potential energy of the charge in the field to the value of this charge:

The potential of the homogeneous field is equal to

where d- distance counted from some zero level.

Potential charge interaction energy q is equal to the field.

Therefore, the work of the field to move the charge from a point with a potential φ 1 to a point with a potential φ 2 is:

The value is called the potential difference or voltage.

The voltage or potential difference between two points is the ratio of the work of the electric field to move the charge from the starting point to the final point to the value of this charge:

[U]=1J/Cl=1V

FIELD STRENGTH AND POTENTIAL DIFFERENCE

When moving charge q along the line of force of the electric field with a strength over a distance Δ d, the field does work

Since, by definition, we get:

Hence, the electric field strength is equal to

So, the strength of the electric field is equal to the change in potential when moving along the line of force per unit length.

If a positive charge moves in the direction of the field line, then the direction of the force coincides with the direction of movement, and the work of the field is positive:

Then , that is, the tension is directed in the direction of decreasing potential.

Tension is measured in volts per meter:

[E]=1 B/m

The field strength is 1 V/m if the voltage between two points of the field line, located at a distance of 1 m, is 1 V.

ELECTRIC CAPACITY

If we independently measure the charge Q, reported to the body, and its potential φ, it can be found that they are directly proportional to each other:

The value C characterizes the ability of the conductor to accumulate an electric charge and is called the electric capacitance. The capacitance of a conductor depends on its size, shape, and the electrical properties of the medium.

The electrical capacity of two conductors is the ratio of the charge of one of them to the potential difference between them:

body capacity is 1 F if, when a charge of 1 C is imparted to it, it acquires a potential of 1 V.

CAPACITORS

Capacitor- two conductors separated by a dielectric, which serve to accumulate an electric charge. The charge of a capacitor is understood as the charge modulus of one of its plates or plates.

The ability of a capacitor to store a charge is characterized by an electrical capacity, which is equal to the ratio of the capacitor's charge to the voltage:

The capacitance of a capacitor is 1 F if, at a voltage of 1 V, its charge is 1 C.

The capacitance of a flat capacitor is directly proportional to the area of ​​the plates S, the permittivity of the medium, and is inversely proportional to the distance between the plates d:

ENERGY OF A CHARGED CAPACITOR.

Precise experiments show that W=CU 2 /2

As q=CU, then

Electric field energy density

where V=Sd is the volume occupied by the field inside the capacitor. Given that the capacitance of a flat capacitor

and the tension on its linings U=Ed

we get:

Example. An electron, moving in an electric field from point 1 through point 2, increased its speed from 1000 to 3000 km/s. Determine the potential difference between points 1 and 2.

One of the basic concepts in electricity is the electrostatic field. Its important property is the work of moving a charge in an electric field, which is created by a distributed charge that does not change in time.

Terms of work

The force in an electrostatic field moves a charge from one place to another. It is completely unaffected by the shape of the trajectory. The definition of force depends only on the position of the points at the beginning and end, as well as on the total amount of charge.

Based on this, we can draw the following conclusion: If the trajectory when moving an electric charge is closed, then all the work of forces in the electrostatic field has a zero value. In this case, the shape of the trajectory does not matter, since the Coulomb forces produce the same work. When the direction in which the electric charge moves is reversed, the force itself also changes its sign. Therefore, a closed trajectory, regardless of its shape, determines the entire work produced by the Coulomb forces, equal to zero.

If several point charges take part in the creation of an electrostatic field at once, then their total work will be the sum of the work performed by the Coulomb fields of these charges. The total work, regardless of the shape of the trajectory, is determined solely by the location of the start and end points.

The concept of potential energy of a charge

Characteristic of the electrostatic field, allows you to determine the potential energy of any charge. In addition, with its help, the work of moving a charge in an electric field is more accurately determined. To obtain this value, it is necessary to select a certain point in space and the potential energy of the charge placed at this point.

A charge placed at any point has a potential energy equal to the work done by the electrostatic field during the movement of the charge from one point to another.

In a physical sense, potential energy is a value for each of two different points in space. At the same time, the work on moving the charge is independent of the paths of its movement and the selected point. The potential of an electrostatic field at a given spatial point is equal to the work done by electric forces when a unit positive charge is removed from this point into infinite space.

The work of the electric field

Any charge that is in an electric field is affected by a force. In this regard, when the charge moves in the field, a certain work of the electric field occurs. How to calculate this work?

The work of an electric field is to transfer electric charges along a conductor. It will be equal to the product of the voltage and the time spent on work.

By applying the formula of Ohm's law, we can get several different versions of the formula for calculating the work of the current:

A = U˖I˖t = I²R˖t = (U²/R)˖t.

In accordance with the law of conservation of energy, the work of the electric field is equal to the change in the energy of a single section of the circuit, and therefore the energy released by the conductor will be equal to the work of the current.

We express in the SI system:

[A] = V˖A˖s = W˖s = J

1 kWh = 3600000 J.

Let's do an experiment. Consider the movement of a charge in the same field, which is formed by two parallel plates A and B and charged opposite charges. In such a field, the lines of force are perpendicular to these plates throughout their length, and when plate A is positively charged, then E will be directed from A to B.

Suppose that a positive charge q has moved from point a to point b along an arbitrary path ab = s.

Since the force that acts on the charge that is in the field will be equal to F \u003d qE, the work done when the charge moves in the field according to a given path will be determined by the equality:

A = Fs cos α, or A = qFs cos α.

But s cos α = d, where d is the distance between the plates.

It follows from here: A = qEd.

Let's say now the charge q will move from a and b to essentially acb. The work of the electric field done on this path is equal to the sum of the work done on its individual sections: ac = s₁, cb = s₂, i.e.

A = qEs₁ cos α₁ + qEs₂ cos α₂,

A = qE(s₁ cos α₁ + s₂ cos α₂,).

But s₁ cos α₁ + s₂ cos α₂ = d, and hence in this case A = qEd.

In addition, suppose that the charge q moves from a to b along an arbitrary curved line. To calculate the work done on a given curvilinear path, it is necessary to stratify the field between plates A and B with a certain number of which will be so close to each other that individual sections of the path s between these planes can be considered straight.

In this case, the work of the electric field produced on each of these segments of the path will be equal to A₁ = qEd₁, where d₁ is the distance between two adjacent planes. And the total work on the whole path d will be equal to the product of qE and the sum of distances d₁ equal to d. Thus, as a result of a curvilinear path, the perfect work will be equal to A = qEd.

The examples we have considered show that the work of an electric field in moving a charge from one point to another does not depend on the shape of the path of movement, but depends solely on the position of these points in the field.

In addition, we know that the work done by gravity when moving a body along an inclined plane of length l will be equal to the work done by the body when falling from a height h, and the height of the inclined plane. This means that work, or, in particular, work during the movement of a body in a gravitational field, also does not depend on the shape of the path, but depends only on the difference in heights of the first and last points of the path.

So it can be proved that not only a homogeneous, but also any electric field can have such an important property. Gravity has a similar property.

The work of an electrostatic field in moving a point charge from one point to another is determined by the linear integral:

A₁₂ = ∫ L₁₂q (Edl),

where L₁₂ is the trajectory of the charge, dl is the infinitesimal displacement along the trajectory. If the contour is closed, then the symbol ∫ is used for the integral; in this case, it is assumed that the direction of traversal of the contour is selected.

The work of electrostatic forces does not depend on the shape of the path, but only on the coordinates of the first and last points of movement. Therefore, the field strengths are conservative, while the field itself is potential. It is worth noting that the work of any one along a closed path will be equal to zero.