Free electromagnetic oscillations in an oscillatory circuit. Oscillatory circuit. Thomson's formula Oscillating circuit electromagnetic oscillations Thomson's formula

>> An equation describing the processes in an oscillatory circuit. Period of free electrical oscillations

§ 30 EQUATION DESCRIBING PROCESSES IN THE OSCILLATORY CIRCUIT. PERIOD OF FREE ELECTRIC OSCILLATIONS

Let us now turn to the quantitative theory of processes in an oscillatory circuit.

An equation describing the processes in an oscillatory circuit. Consider an oscillatory circuit, the resistance R of which can be neglected (Fig. 4.6).

The equation describing the free electrical oscillations in the circuit can be obtained using the law of conservation of energy. The total electromagnetic energy W of the circuit at any time is equal to the sum of its energies of the magnetic and electric fields:

This energy does not change over time if its resistance R of the circuit is zero. Hence, the time derivative of the total energy is zero. Therefore, the sum of the time derivatives of the energies of the magnetic and electric fields is equal to zero:

The physical meaning of equation (4.5) is that the rate of change in the energy of the magnetic field is equal in absolute value to the rate of change in the energy of the electric field; the "-" sign indicates that as the energy of the electric field increases, the energy of the magnetic field decreases (and vice versa).

Calculating the derivatives in equation (4.5), we get 1

But the time derivative of the charge is the current strength at a given time:

Therefore, equation (4.6) can be rewritten in the following form:

1 We calculate derivatives with respect to time. Therefore, the derivative (і 2) "is not just equal to 2 i, as it would be when calculating the derivative but i. It is necessary to multiply 2 i by the derivative i" of the current strength with respect to time, since the derivative of a complex function is calculated. The same applies to the derivative (q 2)".

The derivative of the current with respect to time is nothing but the second derivative of the charge with respect to time, just as the derivative of velocity with respect to time (acceleration) is the second derivative of the coordinate with respect to time. Substituting into equation (4.8) i "= q" and dividing the left and right parts of this equation by Li, we obtain the main equation describing free electrical oscillations in the circuit:

Now you can fully appreciate the significance of the efforts that have been expended to study the oscillations of a ball on a spring and a mathematical pendulum. After all, equation (4.9) does not differ in anything, except for the notation, from equation (3.11), which describes the vibrations of a ball on a spring. Replacing x with q, x" with q", k with 1/C, and m with L in equation (3.11), we obtain equation (4.9) exactly. But equation (3.11) has already been solved above. Therefore, knowing the formula describing the oscillations of a spring pendulum, we can immediately write down a formula for describing the electrical oscillations in the circuit.

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An electrical circuit consisting of an inductor and a capacitor (see figure) is called an oscillatory circuit. In this circuit, peculiar electrical oscillations can occur. Let, for example, at the initial moment of time we charge the plates of the capacitor with positive and negative charges, and then let the charges move. If the coil were not present, the capacitor would begin to discharge, an electric current would appear in the circuit for a short time, and the charges would disappear. This is where the following happens. First, due to self-induction, the coil prevents the increase in current, and then, when the current begins to decrease, it prevents its decrease, i.e. maintains current. As a result, the self-induction EMF charges the capacitor with reverse polarity: the plate that was initially positively charged acquires a negative charge, the second becomes positive. If there is no loss of electrical energy (in the case of low resistance of the circuit elements), then the magnitude of these charges will be the same as the magnitude of the initial charges of the capacitor plates. In the future, the movement of the process of moving charges will be repeated. Thus, the movement of charges in the circuit is an oscillatory process.

To solve the problems of the exam, devoted to electromagnetic oscillations, you need to remember a number of facts and formulas regarding the oscillatory circuit. First, you need to know the formula for the oscillation period in the circuit. Secondly, to be able to apply the law of conservation of energy to the oscillatory circuit. And finally (although such tasks are rare), be able to use the dependence of the current through the coil and the voltage across the capacitor from time to time.

The period of electromagnetic oscillations in the oscillatory circuit is determined by the relation:

where and are the charge on the capacitor and the current in the coil at this point in time, and are the capacitance of the capacitor and the inductance of the coil. If the electrical resistance of the circuit elements is small, then the electrical energy of the circuit (24.2) remains practically unchanged, despite the fact that the charge of the capacitor and the current in the coil change over time. From formula (24.4) it follows that during electrical oscillations in the circuit, energy transformations occur: at those moments in time when the current in the coil is zero, the entire energy of the circuit is reduced to the energy of the capacitor. At those moments of time when the charge of the capacitor is zero, the energy of the circuit is reduced to the energy of the magnetic field in the coil. Obviously, at these moments of time, the charge of the capacitor or the current in the coil reaches its maximum (amplitude) values.

With electromagnetic oscillations in the circuit, the charge of the capacitor changes over time according to the harmonic law:

standard for any harmonic vibrations. Since the current in the coil is the derivative of the charge of the capacitor with respect to time, from formula (24.4) one can find the dependence of the current in the coil on time

In the exam in physics, tasks for electromagnetic waves are often offered. The minimum knowledge required to solve these problems includes an understanding of the basic properties of an electromagnetic wave and knowledge of the scale of electromagnetic waves. Let us briefly formulate these facts and principles.

According to the laws of the electromagnetic field, an alternating magnetic field generates an electric field, an alternating electric field generates a magnetic field. Therefore, if one of the fields (for example, electric) starts to change, a second field (magnetic) will arise, which then again generates the first (electric), then again the second (magnetic), etc. The process of mutual transformation into each other of electric and magnetic fields, which can propagate in space, is called an electromagnetic wave. Experience shows that the directions in which the vectors of the electric and magnetic field strengths fluctuate in an electromagnetic wave are perpendicular to the direction of its propagation. This means that electromagnetic waves are transverse. In Maxwell's theory of the electromagnetic field, it is proved that an electromagnetic wave is created (radiated) by electric charges as they move with acceleration. In particular, the source of an electromagnetic wave is an oscillatory circuit.

The length of an electromagnetic wave, its frequency (or period) and propagation velocity are related by a relation that is valid for any wave (see also formula (11.6)):

Electromagnetic waves in vacuum propagate at a speed = 3 10 8 m/s, the speed of electromagnetic waves in the medium is less than in vacuum, and this speed depends on the frequency of the wave. This phenomenon is called wave dispersion. An electromagnetic wave has all the properties of waves propagating in elastic media: interference, diffraction, and the Huygens principle is valid for it. The only thing that distinguishes an electromagnetic wave is that it does not need a medium to propagate - an electromagnetic wave can also propagate in a vacuum.

In nature, electromagnetic waves are observed with very different frequencies from each other, and due to this, they have significantly different properties (despite the same physical nature). The classification of the properties of electromagnetic waves depending on their frequency (or wavelength) is called the scale of electromagnetic waves. We give a brief overview of this scale.

Electromagnetic waves with a frequency less than 10 5 Hz (ie, with a wavelength greater than a few kilometers) are called low-frequency electromagnetic waves. Most household electrical appliances emit waves of this range.

Waves with a frequency of 10 5 to 10 12 Hz are called radio waves. These waves correspond to wavelengths in vacuum from several kilometers to several millimeters. These waves are used for radio communications, television, radar, cell phones. The sources of radiation of such waves are charged particles moving in electromagnetic fields. Radio waves are also emitted by free metal electrons, which oscillate in an oscillatory circuit.

The region of the scale of electromagnetic waves with frequencies lying in the range 10 12 - 4.3 10 14 Hz (and wavelengths from a few millimeters to 760 nm) is called infrared radiation (or infrared rays). Molecules of a heated substance serve as a source of such radiation. A person emits infrared waves with a wavelength of 5 - 10 microns.

Electromagnetic radiation in the frequency range 4.3 10 14 - 7.7 10 14 Hz (or wavelengths 760 - 390 nm) is perceived by the human eye as light and is called visible light. Waves of different frequencies within this range are perceived by the eye as having different colors. The wave with the smallest frequency from the visible range 4.3 10 14 is perceived as red, with the highest frequency within the visible range 7.7 10 14 Hz - as violet. Visible light is emitted during the transition of electrons in atoms, molecules of solids heated to 1000 ° C or more.

Waves with a frequency of 7.7 10 14 - 10 17 Hz (wavelength from 390 to 1 nm) are commonly called ultraviolet radiation. Ultraviolet radiation has a pronounced biological effect: it can kill a number of microorganisms, it can cause increased pigmentation of human skin (tanning), and in case of excessive exposure, in some cases it can contribute to the development of oncological diseases (skin cancer). Ultraviolet rays are contained in the radiation of the Sun, they are created in laboratories with special gas-discharge (quartz) lamps.

Beyond the region of ultraviolet radiation lies the region of X-rays (frequency 10 17 - 10 19 Hz, wavelength from 1 to 0.01 nm). These waves are emitted during deceleration in the matter of charged particles accelerated by a voltage of 1000 V or more. They have the ability to pass through thick layers of matter that are opaque to visible light or ultraviolet radiation. Due to this property, X-rays are widely used in medicine for diagnosing bone fractures and a number of diseases. X-rays have a detrimental effect on biological tissues. Due to this property, they can be used to treat oncological diseases, although when exposed to excessive radiation, they are deadly to humans, causing a number of disorders in the body. Due to the very short wavelength, the wave properties of X-rays (interference and diffraction) can only be detected on structures comparable to the size of atoms.

Gamma radiation (-radiation) is called electromagnetic waves with a frequency greater than 10 20 Hz (or a wavelength less than 0.01 nm). Such waves arise in nuclear processes. A feature of -radiation is its pronounced corpuscular properties (i.e., this radiation behaves like a stream of particles). Therefore, radiation is often referred to as a stream of -particles.

IN task 24.1.1 to establish correspondence between units of measurement, we use formula (24.1), from which it follows that the period of oscillations in a circuit with a capacitor with a capacity of 1 F and an inductance of 1 H is equal to seconds (the answer 1 ).

From the chart given in task 24.1.2, we conclude that the period of electromagnetic oscillations in the circuit is 4 ms (the response 3 ).

According to the formula (24.1) we find the oscillation period in the circuit given in task 24.1.3:
(answer 4 ). Note that according to the scale of electromagnetic waves, such a circuit emits waves of the long-wave radio range.

The period of oscillation is the time of one complete oscillation. This means that if at the initial moment of time the capacitor is charged with the maximum charge ( task 24.1.4), then after half a period the capacitor will also be charged with the maximum charge, but with reverse polarity (the plate that was initially positively charged will be negatively charged). And the maximum current in the circuit will be achieved between these two moments, i.e. in a quarter of the period (answer 2 ).

If the inductance of the coil is quadrupled ( task 24.1.5), then according to formula (24.1) the oscillation period in the circuit will double, and the frequency doubled (answer 2 ).

According to formula (24.1), with a fourfold increase in the capacitance of the capacitor ( task 24.1.6) the oscillation period in the circuit is doubled (the answer 1 ).

When the key is closed ( task 24.1.7) in the circuit, instead of one capacitor, two of the same capacitors connected in parallel will work (see figure). And since when the capacitors are connected in parallel, their capacitances add up, the closure of the key leads to a twofold increase in the capacitance of the circuit. Therefore, from formula (24.1) we conclude that the oscillation period increases by a factor (the answer is 3 ).

Let the charge on the capacitor oscillate with a cyclic frequency ( task 24.1.8). Then, according to formulas (24.3) - (24.5), the current in the coil will oscillate with the same frequency. This means that the dependence of the current on time can be represented as . From here we find the dependence of the energy of the magnetic field of the coil on time

It follows from this formula that the energy of the magnetic field in the coil oscillates with twice the frequency, and, therefore, with a period that is half the period of the charge and current oscillations (the answer is 1 ).

IN task 24.1.9 we use the law of conservation of energy for the oscillatory circuit. From formula (24.2) it follows that for the amplitude values ​​of the voltage across the capacitor and the current in the coil, the relation

where and are the amplitude values ​​of the capacitor charge and the current in the coil. From this formula, using relation (24.1) for the oscillation period in the circuit, we find the amplitude value of the current

answer 3 .

Radio waves are electromagnetic waves with specific frequencies. Therefore, the speed of their propagation in vacuum is equal to the speed of propagation of any electromagnetic waves, and in particular, X-rays. This speed is the speed of light ( task 24.2.1- answer 1 ).

As stated earlier, charged particles emit electromagnetic waves when moving with acceleration. Therefore, the wave is not emitted only with uniform and rectilinear motion ( task 24.2.2- answer 1 ).

An electromagnetic wave is an electric and magnetic field that varies in space and time in a special way and supports each other. Therefore the correct answer is task 24.2.3 - 2 .

From the given in the condition tasks 24.2.4 It follows from the graph that the period of this wave is - = 4 μs. Therefore, from formula (24.6) we obtain m (the answer 1 ).

IN task 24.2.5 by formula (24.6) we find

(answer 4 ).

An oscillatory circuit is connected to the antenna of the electromagnetic wave receiver. The electric field of the wave acts on the free electrons in the circuit and causes them to oscillate. If the frequency of the wave coincides with the natural frequency of electromagnetic oscillations, the amplitude of oscillations in the circuit increases (resonance) and can be registered. Therefore, to receive an electromagnetic wave, the frequency of natural oscillations in the circuit must be close to the frequency of this wave (the circuit must be tuned to the frequency of the wave). Therefore, if the circuit needs to be reconfigured from a wave length of 100 m to a wave length of 25 m ( task 24.2.6), the natural frequency of electromagnetic oscillations in the circuit must be increased by 4 times. To do this, according to formulas (24.1), (24.4), the capacitance of the capacitor should be reduced by 16 times (the answer 4 ).

According to the scale of electromagnetic waves (see the introduction to this chapter), the maximum length of those listed in the condition tasks 24.2.7 electromagnetic waves has radiation from the antenna of a radio transmitter (response 4 ).

Among those listed in task 24.2.8 electromagnetic waves, X-ray radiation has a maximum frequency (response 2 ).

The electromagnetic wave is transverse. This means that the vectors of the electric field strength and magnetic field induction in the wave at any time are directed perpendicular to the direction of wave propagation. Therefore, when the wave propagates in the direction of the axis ( task 24.2.9), the electric field strength vector is directed perpendicular to this axis. Therefore, its projection on the axis is necessarily equal to zero = 0 (answer 3 ).

The propagation speed of an electromagnetic wave is an individual characteristic of each medium. Therefore, when an electromagnetic wave passes from one medium to another (or from vacuum to a medium), the speed of the electromagnetic wave changes. And what can be said about the other two parameters of the wave included in the formula (24.6) - the wavelength and frequency. Will they change when the wave passes from one medium to another ( task 24.2.10)? Obviously, the wave frequency does not change when moving from one medium to another. Indeed, a wave is an oscillatory process in which an alternating electromagnetic field in one medium creates and maintains a field in another medium due to precisely these changes. Therefore, the periods of these periodic processes (and hence the frequencies) in one and the other medium must coincide (the answer is 3 ). And since the speed of the wave in different media is different, it follows from the reasoning and formula (24.6) that the wavelength changes when it passes from one medium to another.

In electrical circuits, as well as in mechanical systems such as a spring weight or a pendulum, free vibrations.

Electromagnetic vibrationscalled periodic interrelated changes in charge, current and voltage.

freeoscillations are called those that occur without external influence due to the initially accumulated energy.

compelledare called oscillations in the circuit under the action of an external periodic electromotive force

Free electromagnetic oscillations are periodically repeating changes in electromagnetic quantities (q- electric charge,I- current strength,U- potential difference) occurring without energy consumption from external sources.

The simplest electrical system that can oscillate freely is serial RLC loop or oscillatory circuit.

Oscillatory circuit -is a system consisting of series-connected capacitance capacitorsC, inductorsL and a conductor with resistanceR

Consider a closed oscillatory circuit consisting of an inductance L and containers FROM.

To excite oscillations in this circuit, it is necessary to inform the capacitor of a certain charge from the source ε . When the key K is in position 1, the capacitor is charged to voltage. After switching the key to position 2, the process of discharging the capacitor through the resistor begins R and an inductor L. Under certain conditions, this process can be oscillatory.

Free electromagnetic oscillations can be observed on the oscilloscope screen.

As can be seen from the oscillation graph obtained on the oscilloscope, free electromagnetic oscillations are fading, i.e., their amplitude decreases with time. This is because part of the electrical energy on the active resistance R is converted into internal energy. conductor (the conductor heats up when an electric current passes through it).

Let us consider how oscillations occur in an oscillatory circuit and what changes in energy occur in this case. Let us first consider the case when there are no losses of electromagnetic energy in the circuit ( R = 0).

If you charge the capacitor to a voltage U 0, then at the initial time t 1 =0, the amplitude values ​​of the voltage U 0 and charge q 0 = CU 0 will be established on the capacitor plates.

The total energy W of the system is equal to the energy of the electric field W el:

If the circuit is closed, then current begins to flow. Emf appears in the circuit. self-induction

Due to self-induction in the coil, the capacitor is not discharged instantly, but gradually (since, according to the Lenz rule, the resulting inductive current with its magnetic field counteracts the change in the magnetic flux by which it is caused. That is, the magnetic field of the inductive current does not allow the magnetic flux of the current to instantly increase in the contour). In this case, the current increases gradually, reaching its maximum value I 0 at time t 2 =T/4, and the charge on the capacitor becomes equal to zero.

As the capacitor discharges, the energy of the electric field decreases, but at the same time the energy of the magnetic field increases. The total energy of the circuit after discharging the capacitor is equal to the energy of the magnetic field W m:

At the next moment in time, the current flows in the same direction, decreasing to zero, which causes the capacitor to recharge. The current does not stop instantly after the capacitor is discharged due to self-induction (now the magnetic field of the induction current does not allow the magnetic flux of the current in the circuit to decrease instantly). At the time t 3 \u003d T / 2, the capacitor charge is again maximum and equal to the initial charge q \u003d q 0, the voltage is also equal to the initial U \u003d U 0, and the current in the circuit is zero I \u003d 0.

Then the capacitor discharges again, the current flows through the inductor in the opposite direction. After a period of time T, the system returns to its initial state. Complete oscillation is completed, the process is repeated.

The graph of change in charge and current strength with free electromagnetic oscillations in the circuit shows that the current strength fluctuations lag behind the charge fluctuations by π/2.

At any given time, the total energy is:

With free vibrations, a periodic transformation of electrical energy occurs W e, stored in the capacitor, into magnetic energy W m coil and vice versa. If there are no energy losses in the oscillatory circuit, then the total electromagnetic energy of the system remains constant.

Free electrical vibrations are similar to mechanical vibrations. The figure shows graphs of charge change q(t) capacitor and bias x(t) load from the equilibrium position, as well as current graphs I(t) and load speed υ( t) for one period of oscillation.

In the absence of damping, free oscillations in an electrical circuit are harmonic, that is, they occur according to the law

q(t) = q 0 cos(ω t + φ 0)

Parameters L And C oscillatory circuit determine only the natural frequency of free oscillations and the period of oscillations - Thompson's formula

Amplitude q 0 and initial phase φ 0 are determined initial conditions, that is, the way in which the system was brought out of equilibrium.

For fluctuations in charge, voltage and current, formulas are obtained:

For a capacitor:

q(t) = q 0 cosω 0 t

U(t) = U 0 cosω 0 t

For an inductor:

i(t) = I 0 cos(ω 0 t+ π/2)

U(t) = U 0 cos(ω 0 t + π)

Let's remember main characteristics of oscillatory motion:

q 0, U 0 , I 0 - amplitude is the modulus of the largest value of the fluctuating quantity

T - period- the minimum time interval after which the process is completely repeated

ν - Frequency- the number of oscillations per unit time

ω - Cyclic frequency is the number of oscillations in 2n seconds

φ - oscillation phase- the value standing under the cosine (sine) sign and characterizing the state of the system at any time.

Advances in the study of electromagnetism in the 19th century led to the rapid development of industry and technology, especially with regard to communications. While laying telegraph lines over long distances, engineers encountered a number of unexplained phenomena that prompted scientists to research. So, in the 50s, the British physicist William Thomson (Lord Kelvin) took up the issue of transatlantic telegraphy. Given the failures of the first practitioners, he theoretically investigated the issue of the propagation of electrical impulses along the cable. At the same time, Kelvin received a number of important conclusions, which later made it possible to carry out telegraphy across the ocean. Also in 1853, a British physicist deduces the conditions for the existence of an oscillatory electric discharge. These conditions formed the basis of the whole doctrine of electrical oscillations. In this lesson and other lessons in this chapter, we will look at some of the basics of Thomson's theory of electrical oscillations.

Periodic or near-periodic changes in charge, current, and voltage in a circuit are called electromagnetic vibrations. One more definition can also be given.

Electromagnetic vibrations are called periodic changes in the electric field strength ( E) and magnetic induction ( B).

To excite electromagnetic oscillations, it is necessary to have an oscillatory system. The simplest oscillatory system in which free electromagnetic oscillations can be maintained is called oscillatory circuit.

Figure 1 shows the simplest oscillatory circuit - this is an electrical circuit that consists of a capacitor and a conductive coil connected to the capacitor plates.

Rice. 1. Oscillatory circuit

In such an oscillatory circuit, free electromagnetic oscillations can occur.

free oscillations are called, which are carried out due to the energy reserves accumulated by the oscillatory system itself, without attracting energy from the outside.

Consider the oscillatory circuit shown in Figure 2. It consists of: a coil with an inductance L, capacitor with capacitance C, light bulbs (to control the presence of current in the circuit), a key and a current source. Using a key, the capacitor can be connected either to a current source or to a coil. At the initial moment of time (the capacitor is not connected to a current source), the voltage between its plates is 0.

Rice. 2. Oscillatory circuit

We charge the capacitor by shorting it to a DC source.

When the capacitor is switched to the coil, the lamp lights up for a short time, that is, the capacitor is quickly discharged.

Rice. 3. Graph of the dependence of the voltage between the capacitor plates on time during discharge

Figure 3 shows a graph of the voltage between the capacitor plates versus time. This graph shows the time interval from the moment the capacitor switches to the coil until the moment when the voltage across the capacitor is zero. It can be seen that the voltage changed periodically, that is, oscillations occurred in the circuit.

Consequently, free damped electromagnetic oscillations flow in the oscillatory circuit.

At the initial moment of time (before the capacitor was closed to the coil), all the energy was concentrated in the electric field of the capacitor (see Fig. 4 a).

When the capacitor is closed to the coil, it will begin to discharge. The discharge current of the capacitor, passing through the turns of the coil, creates a magnetic field. This means that there is a change in the magnetic flux surrounding the coil, and an EMF of self-induction occurs in it, which prevents the instantaneous discharge of the capacitor, therefore, the discharge current increases gradually. With an increase in the discharge current, the electric field in the capacitor decreases, but the magnetic field of the coil increases (see Fig. 4 b).

At the moment when the field of the capacitor disappears (the capacitor is discharged), the magnetic field of the coil will be maximum (see Fig. 4 c).

Further, the magnetic field will weaken and a self-induction current will appear in the circuit, which will prevent the decrease in the magnetic field, therefore, this self-induction current will be directed in the same way as the capacitor discharge current. This will overcharge the capacitor. That is, on the lining, where at the beginning there was a plus sign, a minus will appear, and vice versa. The direction of the electric field strength vector in the capacitor will also change to the opposite (see Fig. 4 d).

The current in the circuit will weaken due to the increase in the electric field in the capacitor and will completely disappear when the field in the capacitor reaches its maximum value (see Fig. 4e).

Rice. 4. Processes occurring in one period of oscillations

When the electric field of the capacitor disappears, the magnetic field will again reach its maximum (see Fig. 4g).

The charge of the capacitor will begin due to the induction current. As the charge progresses, the current will weaken, and with it the magnetic field (see Fig. 4h).

When the capacitor is charged, the current in the circuit and the magnetic field will disappear. The system will return to its original state (see Fig. 4 e).

Thus, we have considered the processes occurring in one period of oscillations.

The value of the energy concentrated in the electric field of the capacitor at the initial moment of time is calculated by the formula:

, where

Capacitor charge; C is the capacitance of the capacitor.

After a quarter of the period, the entire energy of the electric field of the capacitor is converted into the energy of the magnetic field of the coil, which is determined by the formula:

where L- coil inductance, I- current strength.

For an arbitrary moment in time, the sum of the energies of the electric field of the capacitor and the magnetic field of the coil is a constant value (if we neglect attenuation):

According to the law of conservation of energy, the total energy of the circuit remains constant, therefore, the time derivative of a constant value will be equal to zero:

Calculating time derivatives, we get:

We take into account that the instantaneous value of the current is the first derivative of the charge with respect to time:

Consequently:

If the instantaneous value of the current is the first derivative of the charge with respect to time, then the derivative of the current with respect to time will be the second derivative of the charge with respect to time:

Consequently:

We have obtained a differential equation, the solution of which will be a harmonic function (the charge depends harmonically on time):

The cyclic oscillation frequency, which is determined by the values ​​​​of the capacitance of the capacitor and the inductance of the coil:

Therefore, the fluctuation of the charge, and hence the current and voltage in the circuit, will be harmonic.

Since the period of oscillation is inversely related to the cyclic frequency, the period is equal to:

This expression is called Thomson's formula.

Bibliography

1. Myakishev G.Ya. Physics: Proc. for 11 cells. general education institutions. - M.: Education, 2010.
2. Kasyanov V.A. Physics. Grade 11: Proc. for general education institutions. - M.: Bustard, 2005.
3. Gendenstein L.E., Dick Yu.I., Physics 11. - M .: Mnemosyne

1. Lms.licbb.spb.ru ().
2. home-task.com().
3. Sch130.ru ().
4. Youtube.com().

Homework

1. What are electromagnetic waves?
2. Questions at the end of paragraph 28, 30 (2) - Myakishev G.Ya. Physics 11 (see the list of recommended readings) ().
3. How is the transformation of energy in the circuit?