The field strength is determined. Electric field strength. The principle of field superposition

Before figuring out how to determine tension electric field, it is imperative to understand the essence of this phenomenon.

Electric field properties

Mobile and stationary charges participate in the creation of an electric field. The presence of the field is manifested in its forceful effect on them. In addition, the field is capable of creating the induction of charges located on the surface of conductors. When a field is created by stationary charges, it is considered a stationary electric field. Another name is electrostatic field. Is one of the varieties electromagnetic field, with the help of which all force interactions occurring between charged particles occur.

How is electric field strength measured?

Tension is a vector quantity that exerts a force on charged particles. The magnitude is defined as the ratio of the force directed from its side to the magnitude of the point test electric charge at a specific point in this field. A test electric charge is introduced into the electric field specifically so that the intensity can be calculated.

In addition to theory, there are practical ways to determine the electric field strength:

In an arbitrary electric field, it is necessary to take a body containing an electric charge. The dimensions of this body must be smaller than the dimensions of the body with the help of which the electric field is generated. For this purpose, you can use a small metal ball with an electrical charge. It is necessary to measure the charge of the ball using an electrometer and place it in the field. The force acting on the ball must be balanced with a dynamometer. After this, readings expressed in newtons are taken from the dynamometer. If the force value is divided by the charge value, you get the voltage value expressed in volts/meter.
The field strength at a certain point, some distance away from the charge, is first determined by measuring the distance between them. Then, the value is divided by the resulting distance squared. A coefficient of 9*10^9 is applied to the result obtained.
In a capacitor, determining the voltage begins with measuring the voltage between its plates using a voltmeter. Next, you need to measure the distance between the plates. The value in volts is divided by the distance between the plates in meters. The result obtained will be the value of the electric field strength.

Tension The electric field is a vector quantity, which means it has a numerical magnitude and direction. The magnitude of the electric field strength has its own dimension, which depends on the method of its calculation.

The electric force of interaction between charges is described as non-contact action, in other words, long-range action takes place, that is, action at a distance. In order to describe such long-range action, it is convenient to introduce the concept of an electric field and, with its help, explain the action at a distance.

Let's take an electric charge, which we will denote by the symbol Q. This electric charge creates an electric field, that is, it is the source of force. Since in the universe there is always at least one positive and at least one negative charge, which act on each other at any, even infinitely distant, distance, then any charge is source of strength, which means it is appropriate to describe the electric field they create. In our case, the charge Q is source electric field and we will consider it precisely as a source of the field.

Electric field strength source charge can be measured using any other charge located somewhere in its vicinity. The charge that is used to measure the electric field strength is called test charge, as it is used to test field strength. A test charge has a certain amount of charge and is indicated by the symbol q.

When placed trial charge into an electric field source of strength(charge Q), trial the charge will experience the action of an electrical force - either attraction or repulsion. Force can be denoted as is usually accepted in physics by the symbol F. Then the magnitude of the electric field can be defined simply as the ratio of the force to the magnitude trial charge.

If the electric field strength is indicated by the symbol E, then the equation can be rewritten in symbolic form as

The standard metric units for measuring electric field strength arise from its definition. Thus, the electric field strength is defined as a force equal to 1 Newton(H) divided by 1 Pendant(Cl). Electric field strength is measured in Newton/Coulomb or otherwise N/Kl. In the SI system it is also measured in Voltmeter. To understand the essence of such a subject, how much more important is the dimension in the metric system in N/C, because this dimension reflects the origin of such a characteristic as field strength. The Volt/Meter notation makes the concept of field potential (Volt) basic, which is useful in some areas, but not in all.

The above example involves two charges Q (source) And q trial. Both of these charges are a source of force, but which one should be used in the above formula? There is only one charge in the formula and that is trial charge q(not source).

Doesn't depend on quantity trial charge q. This may seem confusing at first glance, if you really think about it. The trouble is that not everyone has the useful habit of thinking and remains in the so-called blissful ignorance. If you don’t think, then you won’t have this kind of confusion. So how does the electric field strength not depend on q, If q present in the equation? Great question! But if you think about it a little, you can answer this question. Increase in quantity trial charge q- say, 2 times - the denominator of the equation will also increase 2 times. But in accordance with Coulomb's Law, increasing the charge will also proportionally increase the generated force F. The charge will increase 2 times, then the strength F will increase by the same amount. Since the denominator in the equation increases by a factor of two (or three, or four), the numerator will increase by the same amount. These two changes cancel each other out, so we can safely say that the electric field strength does not depend on the amount trial charge.

Thus, no matter how many trial charge q used in the equation, electric field strength E at any given point around the charge Q (source) will be the same when measured or calculated.

Learn more about the electric field strength formula

Above we touched on the definition of electric field strength in how it is measured. Now we will try to explore a more detailed equation with variables in order to more clearly imagine the very essence of calculating and measuring the electric field strength. From the equation we can see exactly what is affected and what is not. To do this, we first need to return to the equation of Coulomb's Law.

Coulomb's law states that electric force F between two charges is directly proportional to the product of the number of these charges and inversely proportional to the square of the distance between their centers.

If we add our two charges into the equation of Coulomb's Law Q (source) And q (trial charge), then we get the following entry:

If the expression for electric force F how is it determined Coulomb's law substitute into the equation for electric field strength E which is given above, then we get the following equation:

note that trial charge q was reduced, that is, removed from both the numerator and the denominator. New formula for electric field strength E expresses field strength in terms of two variables that influence it. Electric field strength depends on the amount of initial charge Q and from the distance from this charge d to a point in space, that is, a geometric location in which the value of tension is determined. Thus, we have the opportunity to characterize the electric field through its intensity.

Inverse square law

Like all formulas in physics, formulas for electric field strength can be used to algebraic solving problems (problems) of physics. Just like any other formula in its algebraic notation, you can study the formula for electric field strength. Such research contributes to a deeper understanding of the essence of a physical phenomenon and the characteristics of this phenomenon. One of the features of the field strength formula is that it illustrates the inverse quadratic relationship between the electric field strength and the distance to a point in space from the field source. The strength of the electric field created in the charge source Q inversely proportional to the square of the distance from the source. Otherwise they say that the desired quantity inversely proportional to the square .

The electric field strength depends on the geometric location in space, and its value decreases with increasing distance. So, for example, if the distance increases by 2 times, then the intensity will decrease by 4 times (2 2), if the distances between decrease by 2 times, then the electric field strength will increase by 4 times (2 2). If the distance increases by 3 times, then the electric field strength decreases by 9 times (3 2). If the distance increases by 4 times, then the electric field strength decreases by 16 (4 2).

Direction of the electric field strength vector

As mentioned earlier, electric field strength is a vector quantity. Unlike a scalar quantity, a vector quantity is not fully described unless its direction is specified. The magnitude of the electric field vector is calculated as the magnitude of the force at any trial charge located in an electric field.

The force acting on trial the charge can be directed either towards the charge source or directly away from it. The exact direction of the force depends on the signs of the test charge and the source of the charge, whether they have the same sign of charge (repulsion occurs) or their signs are opposite (attraction occurs). To solve the problem of the direction of the electric field vector, whether it is directed towards the source or away from the source, rules were adopted that are used by all scientists in the world. According to these rules, the direction of the vector is always from a charge with a positive polarity sign. This can be represented in the form of lines of force that come out of charges of positive signs and enter charges of negative signs.

Objective of the lesson: give the concept of electric field strength and its definition at any point in the field.

Lesson objectives:

formation of the concept of electric field strength; give the concept of tension lines and a graphical representation of the electric field;
teach students to apply the formula E=kq/r 2 in solving simple problems of calculating tension.

The electric field is special shape matter, the existence of which can be judged only by its action. It has been experimentally proven that there are two types of charges around which there are electric fields characterized by lines of force.

When depicting the field graphically, it should be remembered that the electric field strength lines:

do not intersect with each other anywhere;
have a beginning on a positive charge (or at infinity) and an end on a negative charge (or at infinity), i.e. they are open lines;
between charges are not interrupted anywhere.

Fig.1

Positive charge lines:

Fig.2

Negative charge lines:

Fig.3

Field lines of interacting charges of the same name:

Fig.4

Field lines of unlike interacting charges:

Fig.5

The strength characteristic of the electric field is intensity, which is denoted by the letter E and has units of measurement or. Tension is a vector quantity, as it is determined by the ratio of the Coulomb force to the value of a unit positive charge

As a result of transforming the formula of Coulomb's law and the intensity formula, we have the dependence of the field strength on the distance at which it is determined relative to a given charge

Where: k– proportionality coefficient, the value of which depends on the choice of units of electric charge.

In the SI system N m 2 / Cl 2,

where ε 0 is the electrical constant equal to 8.85·10 -12 C 2 /N m 2 ;

q – electric charge (C);

r is the distance from the charge to the point at which the voltage is determined.

The direction of the tension vector coincides with the direction of the Coulomb force.

An electric field whose strength is the same at all points in space is called uniform. In a limited region of space, the electric field can be considered approximately uniform if the field strength within this region changes slightly.

The total field strength of several interacting charges will be equal to geometric sum tension vectors, which is the principle of field superposition:

Let's consider several cases of determining tension.

1. Let two opposite charges interact. Let's place a point positive charge between them, then at this point there will be two voltage vectors directed in the same direction:

According to the principle of field superposition, the total field strength at a given point is equal to the geometric sum of the strength vectors E 31 and E 32.

The tension at a given point is determined by the formula:

E = kq 1 /x 2 + kq 2 /(r – x) 2

where: r – distance between the first and second charge;

x is the distance between the first and point charge.

Fig.6

2. Consider the case when it is necessary to find the voltage at a point distant at a distance a from the second charge. If we take into account that the field of the first charge is greater than the field of the second charge, then the intensity at a given point of the field is equal to the geometric difference in intensity E 31 and E 32.

The formula for tension at a given point is:

E = kq1/(r + a) 2 – kq 2 /a 2

Where: r – distance between interacting charges;

a is the distance between the second and point charge.

Fig.7

3. Let's consider an example when it is necessary to determine the field strength at a certain distance from both the first and second charge, in this case at a distance r from the first and at a distance b from the second charge. Since like charges repel, and unlike charges attract, we have two tension vectors emanating from one point, then to add them we can apply the method; the opposite corner of the parallelogram will be the total tension vector. We find the algebraic sum of vectors from the Pythagorean theorem:

E = (E 31 2 + E 32 2) 1/2

Hence:

E = ((kq 1 /r 2) 2 + (kq 2 /b 2) 2) 1/2

Fig.8

Based on this work, it follows that the intensity at any point in the field can be determined by knowing the magnitude of the interacting charges, the distance from each charge to a given point and the electrical constant.

4. Reinforcing the topic.

Test work.

Option #1.

1. Continue the phrase: “electrostatics is...

2. Continue the phrase: an electric field is….

3. How are the field lines of intensity of this charge directed?

4. Determine the signs of the charges:

5. Indicate the tension vector.

Homework tasks:

1. Two charges q 1 = +3·10 -7 C and q 2 = −2·10 -7 C are in a vacuum at a distance of 0.2 m from each other. Determine the field strength at point C, located on the line connecting the charges, at a distance of 0.05 m to the right of the charge q 2.

2. At a certain point in the field, a charge of 5·10 -9 C is acted upon by a force of 3·10 -4 N. Find the field strength at this point and determine the magnitude of the charge creating the field if the point is 0.1 m away from it.

>>Physics: Electric field strength. Principle of field superposition

It is not enough to assert that an electric field exists. It is necessary to introduce a quantitative characteristic of the field. After this, electric fields can be compared with each other and their properties can continue to be studied.
An electric field is detected by the forces acting on a charge. It can be argued that we know everything we need about the field if we know the force acting on any charge at any point in the field.
Therefore, it is necessary to introduce a characteristic of the field, knowledge of which will allow us to determine this force.
If you alternately place small charged bodies at the same point in the field and measure the forces, you will find that the force acting on the charge from the field is directly proportional to this charge. Indeed, let the field be created by a point charge q 1. According to Coulomb's law (14.2) on the charge q 2 there is a force proportional to the charge q 2. Therefore, the ratio of the force acting on a charge placed at a given point in the field to this charge for each point in the field does not depend on the charge and can be considered as a characteristic of the field. This characteristic is called electric field strength. Like force, field strength is vector quantity; it is denoted by the letter . If a charge placed in a field is denoted by q instead of q 2, then the tension will be equal to:

The field strength at a given point is equal to the ratio of the force with which the field acts on a point charge placed at this point to this charge.
Hence the force acting on the charge q from the electric field side, is equal to:

The direction of the vector coincides with the direction of the force acting on the positive charge and is opposite to the direction of the force acting on the negative charge.
Field strength of a point charge. Let's find the electric field strength created by a point charge q 0. According to Coulomb's law, this charge will act on a positive charge q with a force equal to

Field strength modulus of a point charge q 0 at a distance r it is equal to:

The intensity vector at any point of the electric field is directed along the straight line connecting this point and the charge ( Fig.14.7) and coincides with the force acting on a point positive charge placed at a given point.

Principle of field superposition. If several forces act on a body, then, according to the laws of mechanics, the resulting force is equal to the geometric sum of these forces:

Electric charges are acted upon by forces from the electric field. If, when fields from several charges are superimposed, these fields do not have any influence on each other, then the resulting force from all fields must be equal to the geometric sum of the forces from each field. Experience shows that this is exactly what happens in reality. This means that the field strengths add up geometrically.
if at a given point in space various charged particles create electric fields whose strengths etc., then the resulting field strength at this point is equal to the sum of the strengths of these fields:

Moreover, the field strength created by an individual charge is determined as if there were no other charges creating the field.
Thanks to the superposition principle, to find the field strength of a system of charged particles at any point, it is enough to know expression (14.9) for the field strength of a point charge. Figure 14.8 shows how the field strength at a point is determined A, created by two point charges q 1 And q 2 , q 1 >q 2

The introduction of an electric field allows us to divide the problem of calculating the interaction forces of charged particles into two parts. First, the field strength created by the charges is calculated, and then the forces are determined from the known strength. This division of the problem into parts usually makes force calculations easier.

???
1. What is the electric field strength called?
2. What is the field strength of a point charge?
3. How is the charge field strength q 0 directed if q 0>0 ? If q 0<0 ?
4. How is the principle of field superposition formulated?

G.Ya.Myakishev, B.B.Bukhovtsev, N.N.Sotsky, Physics 10th grade

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If you have corrections or suggestions for this lesson,

The electric force of interaction of charges is described as a non-contact action, and in other words, long-range action takes place, that is, action at a distance. In order to describe such long-range action, it is convenient to introduce the concept of an electric field and, with its help, explain the action at a distance.

If the electric field strength is indicated by the symbol E, then the equation can be rewritten in symbolic form as

Thus, no matter how many trial charge q used in the equation, electric field strength E at any given point around the charge Q (source) will be the same when measured or calculated.

Learn more about the electric field strength formula

If we add our two charges into the equation of Coulomb's Law Q (source) And q (trial charge), then we get the following entry:

If the expression for electric force F how is it determined Coulomb's law substitute into the equation for electric field strength E which is given above, then we get the following equation:

The field strength is determined. Electric field strength. The principle of field superposition – Knowledge Hypermarket

Electric field properties

How is electric field strength measured?

Learn more about the electric field strength formula

Inverse square law

Direction of the electric field strength vector

Learn more about the electric field strength formula

Inverse square law

Direction of the electric field strength vector

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