9 10 9 constant. Coincidence of numbers on the clock - what do the same numbers say? The meaning of identical combinations

People have long attributed various meanings to numerical coincidences, and among them, the coincidence of numbers on a clock occupies a special place. After all, everyone knows that based on the date, month and year of birth you can learn a lot about a person, and if some numbers constantly catch your eye, this is definitely some kind of sign.

In the article:

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What does it mean if the numbers on the clock coincide?

Experts in the field believe that numbers have a significant impact on each of us, and it is simply stupid to underestimate the importance of studying them.

12 21 on the clock

Almost everyone has noticed the same numbers on the clock, but few people know that there is an interpreter who can help you decipher what these numbers promise you. The fact is that such coincidences are nothing more than a warning from higher powers. They almost always have something to tell you.

It is especially worth paying attention to such coincidences if they often happen in your life. If they are the same number, you can find the answer in the article about . This is your way of trying to communicate with you. Different numbers mean that you have very good intuition and are able to receive messages from the Universe.

Fortune telling on the clock - the same numbers in the first half of the day

• 00:00 - if your thoughts are pure, you can make a wish, and it will definitely come true. You cannot make wishes that could bring harm to someone; such wishes will not be fulfilled in this case.
• 01:01 - soon you will receive pleasant news from a man.
01:10 - the new business you started will not bring the result you expect.
• 01:11 - you will receive a favorable offer. This could be any offer that comes within these 24 hours; it is undesirable to refuse.
• 02:02 - an invitation to visit or another extremely fun event.
• 02:20 - on this day you need to suppress your irritation and not succumb to provocations. This can lead to serious problems.
• 02:22 - you will find out what was hidden from you.
• 03:03 - love awaits you.
• 03:30 - to disappointment or lack of reciprocity.
• 03:33 - luck and success. An extremely happy day awaits you.
• 04:04 - you need to look at the situation that worries you from the other side, and then you will be able to find a solution.
• 04:40 - the day will be unlucky.
• 04:44 - you will be reprimanded by your boss, teacher or older relatives.
• 05:05 - bad things are being planned against you. Your enemies are not asleep; be prepared for the fact that they most likely will not act honestly.
• 05:50 - beware of water and fire. On this day it is better to have as few things to do with them as possible.
• 05:55 - meeting with a wise man.
• 06:06 - if you are single, very soon you will meet your soulmate and get married. If you are married, this day will be very successful.
• 07:07 - you are in danger from a person in uniform, most likely, we are talking about a military man.
• 08:08 - a good day for your career, success awaits you.
• 09:09 - be vigilant, you may suffer from theft. Keep track of your belongings or do not take anything valuable with you on this day.
• 10:01 - meeting a very influential person.
• 10:10 - to change.
• 11:11 - you need to think about possible dependence on a person or bad habits. The Universe is warning you that this could happen to you soon.

The meaning of the same numbers on the clock is the second half of the day

• 12:12 - this day promises success in your personal life.
• 12:21 - an interesting acquaintance with a person of the opposite sex.
• 13:13 - beware of enemies.
• 13:31 - to fulfill a wish.
• 14:14 - luck in love.
• 14:41 - troubles.
• 15:15 - you will receive valuable advice in a difficult situation.
• 15:51 - you can count on a whirlwind romance, but it will be short-lived.
• 16:16 - be careful on the roads and in everything related to transport.
• 17:17 - Beware of robbery or attack by a hooligan. Perhaps you shouldn’t stay out late on this day alone.
• 18:18 - dangers associated with transport await you. Be careful.
• 19:19 - success in all matters that you undertake.

• 20:02 - Beware of quarrels within the family. Throughout the evening and the next day, it is better to be patient and not succumb to the provocations of your spouse or relatives.
• 20:20 - a scandal may break out within the family. Be prepared to keep it to a minimum.
• 21:12 - the beginning of something new. Perhaps we are talking about pregnancy, or maybe you are changing your occupation or working on a new project.
• 21:21 - a passionate romance or a favorable period for restoring relations with a spouse.
• 22:22 - a new acquaintance that will play an important role in your life.
• 23:23 - dangerous connection.
• 23:32 - health problems.

In general, it should be noted that paired clock numbers only have a specific meaning when you notice them by chance. A situation where you specifically wait for some time to get the result you are interested in is not suitable for fortune telling by the clock.

Every person would like to receive an omen from their guardian angel. Angelic numerology is a phenomenon in which higher powers try to establish a connection with a person. Using the magic of numbers, for example, the coincidence of numbers on a clock, they inform us about what is about to happen in our lives, or try to warn us about something.

Who is Doreen Virtue

Doreen Virtue is a practicing philosopher. She specializes in spirituality and human psychology. During her work, the scientist, through personal and professional experience, had the opportunity to communicate with children who have superpowers, the so-called young Lightbearers.

Doreen Virtue - author of the concept of angelic numerology

What is angelic numerology

Messages from higher powers are a kind of predictions for humans, encrypted in numbers. Every day we come across some digital combinations, these could be:

• numbers on cars;
• time on the clock;
• numbering of houses or offices;
• matching dates of birth;
• public transport ticket numbers and much more.

All this may contain hidden information that can change your future.

Doreen Virtue, in many of her publications, shares with readers her experience of how, with the help of numbers, angels communicate with people, conveying important messages to them. The simplest and most famous way is to match the numbers on the clock. But recognizing a secret sign is not enough. The point is to decipher it correctly.

Video: numerology of angels as interpreted by Maxim Fedorov

How do angelic messages manifest themselves and what do they mean?

The “strongest” combinations consist of three identical numbers. Did you notice this number on the house or on the receipt you received after purchase? Find out what the angels want to tell you!

111

Three units is a sign that calls for a quick response. Having seen such a number, you need to build a plan of action with concentration, without panic. It is important not to get confused and bring the matter to the final phase.

With this combination, the angel is trying to awaken your vigilance, warning of any danger or calling on you to concentrate and act on time in an unpredictable situation.

222

A combination of three twos means that you need to be more careful in making decisions. Depending on your actions and words, a certain chain of events may unfold that will affect your entire future life. It is important to show intelligence and resourcefulness to prevent a sad outcome of the situation.

333

Three triplets act as a reminder that your destiny is being watched over by the ascended masters - the age-old guardians of historical events from the beginning of time. They have a powerful influence on the spiritual development of people. For centuries, their words have flown from the lips of different thinkers. Whatever thought comes into your head, it immediately triggers the mechanism for its implementation. Everything is predetermined and practically uneditable.

Three threes mean that your life is powerfully influenced by Higher Powers

444

Three fours represent a symbol of people who have lost themselves, their purpose in life and have gone astray from their intended path. The number represents those who are stuck in gray, hopeless everyday life, completely alone. This sign of the guardian angel encourages you not to lose heart, because you are not alone, there are your loved ones and friends who need you, love you and are waiting to meet you. Take heart, everything will be fine.

555

A combination of three fives means that you will again need all your endurance in solving important matters. Nothing too serious is planned; it will not be difficult for you to repeat the path that has already led you to victories.

If something suddenly happens that you did not expect, you should not worry about it. Take it for granted - and you will be on top again.

666

The mystical and frightening three sixes act as a warning from your guardian angel. You risk slipping and falling from the heights of your many victories. Don't try to get everything now and at once. If you strive for something without looking back, you will achieve nothing and will be left with nothing. Don't chase what you don't really need. Curb your impulse of ambition. Appreciate what you have, hold it tightly and try not to lose it.

Many people associate the triple repetition of six with the sign of the devil. But numerologists explain this number more simply. Combination 666 encrypts the energy of the physical nature of humanity.

777

Three sevens promise amazing success. Even if you haven't planned anything big in the near future, major changes will occur in your life. There is a person nearby who cares about you and strives to please you every minute. Trust him with your destiny and you will never regret it.

Develop, move only forward. On your way, at all intersections only green lights are on. Feel free to open new horizons, believe in yourself - and whatever you set your mind to, you will be able to do it.

Three sevens portend success in everything

888

Three eights are a symbol that is not often paid attention to. The thing is that it appears when everything is excellent with a person. However, do not forget that life is fleeting. Think about conquering new heights, making new plans, and self-improvement. All this will bring you additional pleasure.

Dream, act, achieve, don’t look back at the past. New opportunities are opening up before you, don't miss them.

999

Nine has a special meaning in Doreen Virtue's numerology as it is the number of the angels. This is a symbol of sincerity, loyalty and selflessness, but at the same time - the burden placed on the shoulders of a person responsible for the lives of a large number of people.

The combination of three nines carries a deep meaning. This is a sign of change, a symbol of what has gone and come, of that which will never stop existing - life. Its beginning foreshadows enormous work and systematic progress towards the end, and so on in a circle from the beginning of time.

000

Having noticed a combination of three zeros, a person must realize that he is always under the supervision of the Almighty, and his fate is in the mighty hands of the Creator. The presence of the Higher Powers can be noticed in every thought, in your every word and deed. The Creator knows your whole history from birth and carefully protects you from falls.

To comprehend this is to accept the wisdom of the entire universe. You have to be a messenger for those who need help, be true to your word and to the people who have done you good at least once in your life.

What does the coincidence of numbers on the clock mean?

Sometimes, looking at the clock, we notice interesting combinations of numbers. Such numbers can be perceived as funny coincidences, but Doreen Virtue claims that with their help the angels are trying to tell us important information.

The most famous way to identify messages from angels is to glance at your watch from time to time.

Same numbers

00:00 - the outcome of your activity, in which you have invested a lot of effort and time, now pleases you and bears fruit. You have reached the top, achieved what you have been stubbornly pursuing for most of your life. Slow down and look back, remember where it all began. Evaluate your achievements.

11:11 - if you see such a combination of numbers on the clock at the moment of making a difficult decision, act as you thought about earlier.

22:22 - you made every effort to ensure that your plans began to be realized. Now you can rest, the process has started.

Video: what does it mean if you see the same numbers on the clock

Repeating numbers

If the time on the clock does not consist of four identical digits, but of two repeating numbers, such a sign can also be important. Especially if this is not the first time you have seen such a combination. Check the meaning of the message in the table, perhaps you will be able to understand something extremely important for yourself.

Table: the meaning of repeating numbers on the clock

Time	Meaning
01:01	Concentrate and remember your recent ideas. Perhaps one of them appealed to you the most. Take action! Don’t be afraid of other people’s criticism; people will definitely appear who will support your project. Fight your worries and strive for excellence
02:02	Soon you will receive an invitation to an entertainment event. It is possible to meet old acquaintances, you will see former classmates or celebrate a friend’s wedding
03:03	These numbers mean a meeting of a love nature, and if you already have a loved one, you can expect a romantic date. Are you still looking for your soulmate? Look around. Most likely, there is a person next to you who will become your faithful and reliable companion for life.
04:04	It's time to take off your rose-colored glasses and look at life with clear eyes. It's time to throw away all stereotypes and enjoy every minute of your free time
05:05	A combination of such numbers warns that your ill-wishers are plotting in your absence. Beware of negative influences
06:06	The numbers promise a sudden meeting with a faithful friend who, in times of difficulty, will lend his reliable shoulder, protect you from rash actions and give practical advice.
07:07	Avoid places with large concentrations of military personnel
08:08	Luck will be on your side this day
09:09	Keep a close eye on your belongings; there may be an attack on your property.
10:10	Get rid of obsessive thoughts. Figure out how to apply your ideas
12:12	You are thinking in the right direction. Soon, what you are working on will have a positive effect on your life.
13:13	Think carefully about your decisions, the likelihood of making wrong actions is very high
14:14	A hint that you should concentrate on your desires. It's time to make your dreams come true
15:15	Be careful, in the near future you will be able to make spontaneous decisions that will radically change your life. Changes will be for the better or worse - it depends only on you
16:16	You should engage in spiritual development
17:17	Luck is on your side. Now you are experiencing a bright, successful period of life, when you can realize even the most daring ideas
18:18	It's time for change. If things were not going very well, you can rejoice; changes will lead to a favorable solution to all life situations. Are you doing well anyway? Thank your guardian angel for supporting you
19:19	Time to implement new ideas. You will win easily and confidently. Don't stop, move on, conquering even greater peaks
20:20	The hand of the Lord is guiding you at this time. You are under reliable protection. Courageously overcome all life's obstacles
21:21	Soon you will see the result of your hard work
23:23	You are under the protection of the Wise Lords of the Universe

Mirror numbers as messages from higher powers

The numbers may not just be repetitive. Messages from angels are sometimes encrypted in so-called mirror numbers. These are digital combinations that seem to be the original combined with its reflection. They are no less important than the standard repetition of symbols.

Table: the meaning of mirror numbers on the clock

Time	Meaning
01:10	Get ready for a sudden meeting with an old friend or colleague. The outcome of your conversation may lead to a promotion at work, perhaps during the conversation you can learn something very important
02:20	Be careful what you say and to whom. Ill-wishers can turn what you say to your detriment
03:30	If, next to your loved one, you notice that there is no adequate return in response to your care and attention, you should think about whether you need such a relationship at all. And if one negative trait overlaps all the positive ones, then break off the alliance with this person without regret, you do not have a happy future with him
04:40	Do not enter into important deals in the near future. Most likely they will fail
05:50	Angels warn you about a threat to life from water or fire
10:01	A very important meeting with a very authoritative person is planned in your life. Your future will depend on the outcome of this conversation. You should prepare in advance: think about what strengths you can show off, you may have to work on your appearance
12:21	A completely random acquaintance can make drastic changes in your destiny
13:31	A streak of life, full of risk and failed situations, ended happily. Hurry up to the start, time to win!
14:41	You are on the path to success. From now on, luck will favor your affairs
15:51	A new romantic acquaintance will occur in your life, but its outcome will not be successful
20:02	Beware of quarrels with loved ones
21:12	Find a new hobby. You may discover a talent for writing or, for example, cooking desserts. There will be a desire to change yourself. Any ideas you have to improve your life will benefit you
23:32	This combination warns of the occurrence of some disease. Don’t wait for the disease to manifest itself, get an unscheduled medical examination

Other successful combinations of numbers in esotericism

If you constantly come across combinations of numbers that are not repeated and are not mirror numbers, you should still pay attention to them. Especially if you see them everywhere: on car license plates, apartment numbers, etc.

Combinations with one

Combinations of ones and twos (12, 21, 112, 211) carry information that the wishes you made earlier are already beginning to come true. Don't give up your faith, don't lose heart - and success will come to you immediately.

In numbers 1 and 7, the Higher Powers have encrypted words of encouragement for your desire and amazing perseverance. You are on the right track and will soon reach your goal. Do not skimp on words of gratitude to your guardian angel. It's worth paying attention to detail so you don't miss anything.

Numbers containing 1 and 8 promise a quick cure for illnesses. Review your old things, make room for new ones. Pleasant changes will occur in your life, even if you do not actively participate in it. If circumstances have driven you to a dead end and you don’t see any options for solving problems, don’t worry. Soon the time for favorable changes will come, and any situations will be solvable.

Combinations with one and seven mean that you will soon achieve your goal

With a deuce

Combinations of numbers 2 and 3 will provide you with a successful life full of positive emotions. If things are looking bad at this time, don’t be upset. The Universe hears your wishes. They are destined to come true very soon.

A message from angels in numbers containing 2 and 5 attracts good luck. You will achieve success much faster if you focus on the positive side of any event. Be confident in yourself and your actions - and the result will not be long in coming.

With a three

The encrypted message in numbers 3 and 6 promises you the support of the Universe in self-realization. You are on the way to your long-awaited goal. Everything will be aimed at ensuring that your intentions soon come true. But on condition that you share the acquired knowledge with other people.

Numbers that contain the numbers 3 and 7 mean that you are moving in the right direction. The Universe rewards your actions with all sorts of gifts that can be used to implement your plans.

The combination of three and seven is a sign that you are moving in the right direction

With a four

Numbers 4 and 5 play an important role in your destiny. The Universe has responded to your call, and soon positive changes will occur in your life that will put things in order.

In combinations of numbers 4 and 7, your angel sends you encouragement for your correct actions. Higher Powers will support any endeavors, guiding you on the right path.

With an A

If you often see combinations with the numbers 5 and 6, you can expect pleasant surprises from the Universe, including in material terms. Soon you will be pleased with sudden cash profits.

The messages hidden in the numbers 5 and 7 mean omens of positive changes in fate. You will have the opportunity to gain important knowledge and develop spiritual or physical skills. Don't slow down, strive for self-improvement - and success will soon overtake you.

With a six

Do you often notice numbers containing 6 and 7? This way you receive praise from your guardian angel. Strive for your goals, you are on the right track. Develop, gain new knowledge, use it in practice - you will soon be able to realize your desires.

Numbers 6 and 8 tell you that you will soon receive considerable benefits from selling things you don’t need. They will offer you a great price for them. If you are planning to make any major purchase, do not rush to do it. You should get rid of old things in the near future, otherwise you are not guaranteed a favorable outcome of the transaction.

With seven

Messages encrypted by angels in numbers that contain numbers 7 and 8 foretell favorable changes in your life. If you have unresolved issues that you have been constantly putting on the back burner, now is the time to get them out of there. The time has come to resolve them.

Omens in the numbers 7 and 0 indicate that the angels approve of your actions, keep it up! Just don't miss the opportunity to help people who need your help.

Zeros and sevens standing together symbolize that the Higher Powers support you

With eights and nines

Combinations of numbers 8 and 9 indicate that unplanned circumstances will occur in your life. They may not make you particularly happy. But unexpected situations will contribute to your self-improvement. Do not be upset, everything that is done is for your benefit. Stay calm, the Higher Powers are protecting you from troubles.

Messages from numbers 8 and 0 mean that your wishes will soon come true. The Guardian Angel facilitates this. And if in the near future something completely different from what you had in mind happens, do not despair. This means that the opportune moment has not yet arrived. Does this worry you too much? Ask the Higher Powers to give you enough patience not to give up and wait for your dreams to come true.

Angelic numerology allows you to see important messages from the Higher Powers in seemingly random coincidences of numbers. Listen to them and perhaps you will be able to avoid danger or achieve dizzying success.

Physical constants are constants included in equations that describe the laws of nature and the properties of matter. Physical constants appear in theoretical models of observed phenomena in the form of universal coefficients in corresponding mathematical expressions.

Physical constants are divided into two main groups - dimensional and dimensionless constants. The numerical values ​​of dimensional constants depend on the choice of units of measurement. The numerical values ​​of dimensionless constants do not depend on the systems of units and must be determined purely mathematically within the framework of a unified theory. Among the dimensional physical constants, constants should be distinguished that do not form dimensionless combinations with each other; their maximum number is equal to the number of basic units of measurement - these are the fundamental physical constants themselves: the speed of light, Planck’s constant, etc.). All other dimensional physical constants are reduced to combinations of dimensionless constants and fundamental dimensional constants.

Physical constants

Constant	Designation	Meaning	Error, %
Speed ​​of light in vacuum	c	299792458(1,2) m X s -1	0,004
Fine structure constant	a a -1	0,0072973506(60) 137,03604(11)	0,82 0,82
Elementary charge	e	1.6021892(46) x10 -19 TO	2,9
Planck's constant	h ћ=h/2 p	6.626176(36) x10 -34 J X With 1.0545887(57) x10 -34 J X With	5,4 5,4
Avogadro's constant	N A	6.022045(31) x10 23 mole -1	5,1
Electron rest mass	m e	0.9109534(47) x 10 -30 kg 5.4858026(21) x10 -4 A. eat.	5,1 0,38
Ratio of electron charge to its mass	e/m e	1.7588047(49) x10 -11 k/kg -1	2,8
Muon rest mass	m m	1.883566(11) x10 -28 kg 0,11342920(26) A. eat.	5,6 2,3
Proton rest mass	m p	1.6726485(86) x10 -27 kg 1,007276470(11) A. eat.	5,1 0,011
Neutron rest mass	m n	1.6749543(86) x10 -27 kg 1,008665012(37) A. eat.	5,1 0,037
Faraday's constant	F=N A e	9.648456(27) x10 4 k/mol	2,8
Magnetic flux quantum	F 0=h/ 2e	2.0678506(54) x10 -15 wb	2,6
Rydberg constant	R ?	1.097373177(83) x10 -7 m -1	0,075
Bohr radius	a 0=a/4p R ?	0.52917706(44) x10 -10 m	0,82
Compton wavelength of the electron	l c=a 2 /2 R ? l c/ 135 p =a a 0	2.4263089(40) x10 -12 m 3.8615905(64) x10 -13 m	1,6 1,6
Nuclear magneton	m N =eћ/2m p	5.050824(20) x10 -27 J X Tl -1	3,9
Bohr magneton	m B =eћ/2m e	9.274078(36) x10 -24 J X Tl -1	3,9
Magnetic moment of an electron in Bohr magnetons	m e /m b	1,0011596567(35)	0,0035
Magnetic moment of a proton in nuclear magnetons	m p /m N	2,7928456(11)	0,38
Electron magnetic moment	m e	9.284832(36) x10 -24 J X Tl -1	3,9
Proton magnetic moment	m p	1.4106171(55) x10 -26 J X Tl -1	3,9
Magnetic moment of a proton in Bohr magnetons	m p/ m N	1.521032209(16) x10 -3	0,011
Gyromagnetic ratio for proton	g p	2.6751987(75) x10 8 s -1 X Tl -1	2,8
Universal gas constant	R	8,314441(26) J/( K x mole)	31
Boltzmann's constant	k=R/N A	1.380662(44) x10 -23 J/ TO	32
Stefan–Boltzmann constant	s = (p 2 /60) k 4 / ћ 3 s 2	5.67032(71) x10 -8 W X m -2?K -4	125
Gravitational constant	G	6.6720(41) x10 -11 N X m 2 / kg 2	615

Example 18.

A small positively charged ball of mass m = 90 mg is suspended in the air on a silk thread. If an equal but negative charge is placed below the ball at a distance r = 1 cm from it, then the tension in the thread will increase threefold. Determine the charge of the ball. Solution. The suspended ball is initially acted upon by two forces: the force of gravity P, directed vertically downward, and the tension force of the thread T 1, directed upward along the thread. The ball is in equilibrium and, therefore,

After a negative charge has been brought to the ball from below, in addition to the force of gravity P, it is acted upon by a force F k, directed downward and determined by Coulomb’s law (Fig. 4). In this case, the tension force Taking into account equality (1), we write

Expressing in (2) Fк according to Coulomb’s law to the force of gravity P through the body mass m and the acceleration of free fall g we obtain

Let's check the units of the right and left sides of the calculation formula (3):

Let's write down the numerical values ​​in SI: m = 9·10 -5 kg; r = 10 -2 m; eε = 1; g = 9.81 m/s 2 ;

ε 0 = 8.85·10 -12 F/m. Let's calculate the required charge:

Example 19. Solution.

The charge Q 3 is acted upon by two forces: F 1, directed towards the charge Q 1 and F 2, directed towards the charge Q 2. The charge Q 3 will be in equilibrium if the resultant of these forces is zero:

that is, the forces F 1 and F 2 must be equal in magnitude and directed in opposite directions.

The forces will be opposite in direction only if the charge Q 3 is located at a point on a straight line connecting the charges Q 1 and Q 2 (Fig. 5). For equality of forces, it is necessary that the charge Q 3 be closer to the smaller charge Q 2. Since the force vectors F 1 and F 2 are directed along the same straight line, vector equality (1) can be replaced by a scalar one, omitting the minus sign:

Having expressed the forces F 1 and F 2 according to Coulomb’s law, (2) we write in the form

Taking the square root of both sides of the equality, we find

Let us write down the numerical values ​​of the magnitudes included in (3) in SI: Q 1 = 5·10 -9 C; Q 2 = 3·10 -9 C;

d = 0.2 m. Calculations:

Of the two values ​​of the root r 1 = 11.3 cm and r 2 = -11.3 cm, we take the first, since the second does not satisfy the conditions of the problem. So, in order for the charge Q 3 to be in equilibrium, it must be placed on a straight line, connecting charges Q 1 and Q 2 at a distance r = 11.3 cm from charge Q 1 (Fig. 5). Solution.

Example 20.

At the vertices of an equilateral triangle with side a = 20 cm there are charges Q 1 = Q 2 = -10 nC and Q 3 = 20 nC. Determine the force acting on a charge Q = 1 nC located in the center of the triangle.

Three forces act on the charge Q located in the center of the triangle: (Fig. 6). Since the charges Q 1 and Q 2 are equal and located at the same distances from the charge Q, then

where F 1 is the force acting on the charge Q from the side of the charge Q 1 ; F 2 is the force acting on the charge Q from the side of the charge Q 2 . The resultant of these forces

In addition to this force, charge Q experiences the action of force F 3 from charge Q 3 . We find the required force F acting on the charge Q as the resultant of the forces F´ and F 3:

Since F´ and F 3 are directed along the same straight line and in the same direction, this vector equality can be replaced by a scalar one: or, taking into account (2),

Expressing F 1 and F 2 here according to Coulomb’s law, we get

From Fig. 6 it follows that

Taking this into account, formula (3) will take the form:

Let's check the calculation formula (4):

Let's write down the numerical values ​​of magnitude in SI: Q 1 = Q 2 = -1·10 -8 C; Q 3 = 2·10 -8 C; ε = 1; ε 0 = 8.85·10 -12 F/m;

An electric field is created in a vacuum by two point charges Q 1 = 2 nC Q 2 = -3 nC. The distance between the charges is d = 20 cm. Determine: 1) the intensity and 2) the potential of the electric field at a point located at a distance of r 1 = 15 cm from the first and r 2 = 10 cm from the second charge (Fig. 7). Solution.

According to the principle of superposition of electric fields, each charge creates a field regardless of the presence of other charges in space. Therefore, the strength E of the resulting electric field at the desired point can be found as the geometric sum of the strengths E 1 and E 2 of the fields created by each charge separately: . The electric field strengths created in vacuum by the first and second charges are equal, respectively:

Vector E is directed along a straight line connecting charge Q 1 and point A, away from charge Q 1, since it is positive; vector E 2 is directed along a straight line connecting charge Q 2 and point A, towards charge Q 2 since the charge is negative.

The modulus of vector E is found using the cosine theorem:

where α is the angle between vectors E 1 and E 2. From a triangle with sides d, r 1 and r 2 we find

Substituting the expression E 1 from (1), E 2 from (2) into (3), we obtain

Let's write down the numerical values ​​of magnitude in SI: Q 1 = 2·10 -9 C; Q 2 = -3·10 -9 C; d = 0.2 m; r 1 = 0.15 m; r 2 = 0.1 m; ε = 1; ε 0 = 8.85·10 -12 F/m;

Let's calculate the value of cosα using (4):

Let's calculate the required tension:

Note. Charge moduli are substituted into formula (5), since their signs were taken into account when deriving this formula.

2. The potential at point A of the field is equal to the algebraic sum of the potentials created at this point by charges Q 1 and Q 2:

Let's calculate the required potential: Solution.

Example 22.

What is the speed of revolution of an electron around a proton in a hydrogen atom if the orbit of the electrode is considered circular with a radius r = 0.53 10 -8 cm

When an electron rotates in a circular orbit, the centripetal force is the force of electrical attraction between the electron and the proton, i.e. the equality is true

Centripetal force is determined by the formula

where m is the mass of an electron moving in a circle; u is the speed of electron circulation; r is the radius of the orbit. The force F to the interaction of charges according to Coulomb’s law will be expressed by the formula

where Q 1 and Q 1 are the absolute values ​​of the charges; ε - relative dielectric constant; ε 0 - electrical constant. Substituting into (l) the expressions F cs from (2) and F to from (3), and also taking into account that the charge of the proton and electron, denoted by the letter e, is the same, we obtain

Let's write down the numerical values ​​of magnitude in SI:

e = 1.6·10 -19 C;

m = 9.1·10 -31 kg.

Let's calculate the required speed:

Example 23.

The potential φ at a field point located at a distance r = 10 cm from a certain charge Q is equal to 300 V. Determine the charge and field strength at this point. Solution.

The potential of a point in the field created by a point charge is determined by the formula

where ε 0 is the electrical constant; ε - dielectric constant. From formula (1) we express Q:

For any point in the field of a point charge, the equality is true

From this equality the field strength can be found. Let's write down the numerical values ​​of greatness, expressing them in SI:

ε 0 = 8.85·10 -12 F/m.

Let's substitute the numerical values ​​into (2) and (3):

Example 24.

An electron, whose initial velocity u 0 = 2 Mm/s, flew into a uniform electric field with a strength E = 10 kV/m so that the initial velocity vector is perpendicular to the strength lines. Determine the speed of the electron after time t = 1 ns. Solution.

An electron in an electric field is acted upon by a force

where e is the electron charge. The direction of this force is opposite to the direction of the field lines. In this case, the force is directed perpendicular to the speed u 0.

It imparts acceleration to the electron

where m is the electron mass.

where u 1 is the speed that the electron receives under the influence of field forces.

We find the speed u 1 using the formula

Since the speeds u 0 and u 1 are mutually perpendicular, the resulting speed

Substituting the speed expression according to (3) into (4) and taking into account (1) and (2) we obtain:

Let us write down the numerical values ​​of the quantities included in (5) in SI:

e = 1.6·10 -19 C;

m = 9.11·10 -31 kg;

t = 105·10 -9 s;

Let's calculate the required speed:

u 0 = 2·10 6 m/s;

E = 10·10 4 V/m. Solution.

Example 25.

At point M of the field of a point charge Q = 40 nC there is a charge Q 1 = 1 nC. Under the influence of field forces, the charge will move to point N, located twice as far from charge Q as NM. In this case, work A = 0.1 μJ is performed. How far will the charge Q 1 move?

The work of field forces to move a charge is expressed by the formula

where Q 1 is a moving charge; Φ M – potential of point M of the field; Φ N – potential of point N of the field. Since the field is created by a point charge Q, the potentials of the starting and ending points of the path will be expressed by the formulas:

where r M and r N are the distance from charge Q to points M and N. Substituting expressions for φ M and φ N from (2) and (3) into (1), we obtain

According to the conditions of the problem, r N = 2r M. Taking this into account, we obtain r N - r M = r M. Then

Let's write down the numerical values ​​of the quantities in SI:

Q 1 = 1·10 -9 C;

ε 0 = 8.85·10 -12 F/m.

Q = 4·10 -8 C;

A = 1·10 -7 J;

The electron passed through an accelerating potential difference U = 800 V. Determine the speed acquired by the electron. Solution.

According to the law of conservation of energy, the kinetic energy T acquired by the charge (electron) is equal to the work A performed by the electric field when the electron moves:

Work done by electric field forces when moving an electron

where e is the electron charge. Electron kinetic energy

where m is the mass of the electron; u is its speed. Substituting expressions T and A from (2) and (3) into (1), we obtain , where

Let's write down the numerical values ​​of the quantities included in (4), in SI: U=800 V;

e = 1.6·10 -19 C; m = 9.11·10 -31 kg. Let's calculate the required speed:

Example 27. Solution.

A flat capacitor, the distance between the plates of which d 1 = 3 cm, is charged to a potential difference U 1 = 300 V and is disconnected from the source.

What will be the voltage on the plates of the capacitor if its plates are moved apart to a distance d 2 = 6 cm?

Before the plates move apart, the capacitance of a parallel-plate capacitor

where ε is the dielectric constant of the substance filling the space between the capacitor plates; ε 0 - electrical constant;

S is the area of ​​the capacitor plates. Capacitor plate voltage where Q is the charge of the capacitor. Substituting into (2) the expression for the capacitance of the capacitor from (1), we find

Similarly, we obtain the voltage between the plates after they move apart:

In expressions (3) and (4), the charge Q is the same, since the capacitor is disconnected from the voltage source and no charge loss occurs. Dividing term by term (3) by (4) and making reductions, we get

where Solution.

Let's write down the numerical values ​​in SI: U 1 = 300 V; d 1 = 0.03 m;

d 2 = 0.06 m. Let's calculate Example 28.A flat capacitor with an area of ​​plates S = 50 cm 2 and a distance between them d = 2 mm is charged to a potential difference U = 100 V. The dielectric is porcelain. Determine the field energy and volumetric field energy density of the capacitor. The energy of a capacitor can be determined by the formula According to the Stefan-Boltzmann law energetic luminosity

(emissivity) absolutely

black body is proportional

T4:

Re T4,

On the other hand, this energy emitted per unit time per unit surface of a black body:

R e W S t.

Then the energy emitted during time t:

W Rе S t T4 S t

. Let's do the calculations:		W 5.67 108 2.0736 1012 8 104 60 5643.5 5.64(kJ).		The wavelength corresponding to the maximum energy
t 1 s				radiation, is inversely proportional to temperature
S 1cm2		10 4 m		re T (Wien displacement law):
R e = ?

where b 2.9 103 m K is the first Wien constant, T is the absolute temperature.

Tb,

Energy emitted2 per unit time from unit surface –

energetic luminosity R e according to the law Stefan-Boltzmann:

(emissivity) absolutely

where 5.67 10 8 W/(m2 K-4) is the Stefan-Boltzmann constant. Substituting (1) into (2) we obtain in the SI system (W/m2):

We need to go outside the system. Then we take into account that 1m = 100 cm, and 1m2 = 104 cm2, i.e. 1cm2 = 10-4 m2. We get energetic luminosity outside the system:

Let's substitute the numerical values:

R e 5.67 10

3094 (V

t/cm2 ).

Answer: R e = 3094 W/cm2.

Note: The surface area of ​​25 cm2 is given in order to confuse the student, in other words, to test the strength of the student’s knowledge of the theory.

Taking the thermal emissivity coefficient a t of coal at temperature

T 600 K equal to 0.8, determine:

1) energetic luminosity R e from coal;

2) energy W emitted from a coal surface with an area of ​​5 cm2 in a time of 10 minutes.

a T 0.8				1. According to the Stefan-Boltzmann law, the energy
T 600K		5·10-4 m2		tic luminosity (emissivity) greybody
S 5cm2				proportional to T 4:
t 10 min				R ec a TR ea TT 4,
				where 5.67 10 8 W/(m2 K4) is Stefan’s constant
1) R e s ?
2)W?				Boltzmann.
				Let's do the calculations:

R e s 0.8 5.67 108 1296 108 5879 5.88(kW/m2).

2. For equilibrium gray body radiation, radiation flux (power):

Фe Re with S,

where S is the surface area of ​​the body. Energy emitted over time:

W e t. Then:

W R e s S t . Let's do the calculations:

W 5879 5 104 600 1764 1.76(kJ). Answer: 1. R e s 5.88 kW/m 2 ;

The muffle furnace consumes power P 1 kW. The temperature T of its inner surface with an open hole of area S 25 cm2 is equal to 1.2 kK. Assuming that the furnace opening radiates as a black body, determine how much of the power is dissipated by the walls.

Energetic luminosity (emissivity) R e black body - energy

The energy emitted per unit time per unit surface area of ​​an absolutely black body is proportional to the fourth power of the absolute temperature of the body

T 4, expressed by the Stefan-Boltzmann law:

(emissivity) absolutely

where 5.67 10 8 W/(m2 K4) is the Stefan-Boltzmann constant. From here:

P isS T 4 .

Part of the dissipated power is the difference between the power consumed by the furnace and the radiation power:

							P S T 4,
	Pac					S T 4
								8 1,24 1012 25 10
										1 294 10 3

We can conventionally assume that the Earth radiates as a gray body located at a temperature T 280K. Determine the thermal emissivity coefficient t

Earth, if the energy luminosity R e from its surface is 325

kJ/(m2 h).
T 280K				The earth radiates like a gray body.
R e s 325 kJ/(m2 h)		90.278J/(m2 s)		Thermal coefficient	radiation
				(degree of blackness) of the gray body is from-
and t - ?
				carrying energy	luminosity

gray body to the energetic luminosity of black body, and is found by the formula:

a R e s.

T R e

Stefan-Boltzmann law for absolute black bodies, as if the Earth were a completely black body:

Re T4,

where 5.67 10 8 W/(m2 K4) is the Stefan-Boltzmann constant. Let's substitute into the thermal emissivity coefficient:

aT

Re s

T 4

5,67 10 8

Answer: a T

0,259 .

Power

P radiation from a ball with radius R 10 cm at a certain constant

at a given temperature T is equal to 1 kW. Find this temperature, considering the ball gray

body with emissivity coefficient a T 0.25.

P 1 kW

Gray radiation power (flux) body is a product

R 10cm

energy luminosity of the ball per surface area S:

P Ф Rс S.

Surface area S of the ball:

4 R 2 .

Energetic luminosity (emissivity) R e from the gray body expresses

is governed by the Stefan-Boltzmann law:

Re s

aT T4,

where 5.67 10 8 W/(m2 K4) is the Stefan-Boltzmann constant. Then the radiation power:

P aT T4 4 R2 .

Taking into account all formulas, body surface temperature:

			4 aT R2
			4 0,25 5,67 10 8			3,14 10 2

The answer is T 866K.

The temperature of the tungsten filament in a twenty-five-watt electric lamp is 2450K, and its radiation is 30% of the radiation of a black body at the same surface temperature. Find the surface area S of the filament.

T 2450 K		The power consumed by the filament goes to radiation with a flat
P 25 W		Consider S as a gray body, i.e. the radiation flux is determined by
a T 0.3
		P = Fe = Re S.
		Energetic luminosity(emissivity) gray te-

la according to the Stefan–Boltzmann law:

R e =a T σT4,

where 5.67 10 8 W/(m2 K4) is the Stefan-Boltzmann constant, T is the absolute temperature.

Then power consumption:

R a T 4 S.
Radiation area from here:
	aT T4
Let's substitute the numerical values:
			0,41 10 4	m2 = 0.41 cm2.
	0,3 5,67 10 8 24504

Answer: S = 0.41 cm2.

The maximum spectral density of energetic luminosity (r, T)max of the bright star Arcturus occurs at a wavelength of 580 nm. Assuming that the star emits as a black body, determine the temperature T of the star's surface.

m 580 nm		580·10-9 m		The temperature of the radiating surface can
				be determined from Wien's displacement law:

where b 2.9 10 3 m·K is the first Wien constant. Let us express the temperature T from here:

Tb.

Let's calculate the resulting value:

2,9 10 3

5000K 5(kK).

580 10 9

Answer: T 5 kK.

Due to changes in black body temperature, the maximum spectral

emissivity densities (r, T)max

shifted from 1 to 2.4 µm

on 2

0.8 µm.

How and by how many times the energetic luminosity changed

R e body and maxi-

minimum spectral density of energy luminosity (r, T)max?

2.4µm

2.4·10-9 m

Energetic luminosity

0.8·10-9 m

activity) R e of a black body - energy emitted

0.8µm

per unit time unit surface area absolute

Re 2

lute of the black body, proportional to the fourth

Re 1

(r ,T ) max 2

degree of absolute body temperature

T 4, you-

is expressed by the Stefan-Boltzmann law:

(r ,T ) max1

(emissivity) absolutely

where 5.67 10 8 W/(m2 K4) is the Stefan-Boltzmann constant.

The temperature of the radiating surface can be determined from Wien's displacement law:

m T b ,

where b 2.9 10 3 m·K is the first Wien constant. Expressing the temperature T from here:

and substituting it into formula (1), we get:

and b

are constants, then the energetic luminosity

R e depends

only from

Then the energetic luminosity will increase by:

Re 2

2.4nm

Re 1

0.8nm

2) Maximum spectral density of energy luminosity is proportional to the fifth power of Kelvin temperature and is expressed by the formula Wien's 2nd law:

			CT 5

where coefficient C 1.3 10 5 W/(m3 ·K5) is the constant of Wien’s second law. Let us express the temperature T from Wien's displacement law:

Tb.

Substituting the resulting temperature expression into formula (3), we find:

	(r ,T ) maxC

Since the spectral density is inversely proportional to the wavelength in

fifth degree

We find that change in density from the relation:

2.4nm

(r ,T ) max1

0.8nm

Answer: increased: by 81 times the energy luminosity R e and by 243 times the maximum spectral density of energy luminosity (r, T)max.

The radiation of the Sun is close in its spectral composition to the radiation of a completely black body, for which the maximum emissive speciality occurs at a wavelength of 0.48 μm. Find the mass lost by the Sun every second due to radiation.

m 0.48 µm

0.48·10-6 m

Mass lost by the Sun at any time

t 1 s

we find from Einstein's law: W mc 2:

R C 6.95 108 m

m c 2,

where c is the speed of light.

Energy emitted during time t (see derivation).

task #2):

W T 4

S t ,

where 5.67 10 8 W/(m2 K4) is the Stefan-Boltzmann constant.

Taking into account the fact that the surface area of ​​the Sun as a sphere

S 4 R2

temperature T

according to Wien's displacement law formula (2) will take the form:

4 R C t,

where b 2.9 10 3 m·K is the first Wien constant.

Substituting (3) into (1) we get:

4 R C t

Mass lost by the Sun every second:

4 R C

Let's substitute the numerical values:

2,9 10 3

10 8

4 6,95 108

0,48 10 6

3 108

3441,62 108

6041,7 4

5.1 109 (kg/s).

9 1016

600 nm; 2)

energetic luminosity R e in the wavelength range from

1,590 nm up to

2610 nm. Accept that the average spectral density of the body's energy luminosity in this interval is equal to the value found for the wavelength

T 2 kK

1) . Spectral energy density

600·10-9 m

luminosity, according to Planck's formula:

590·10-9 m

2 hс 2

610 nm

1) (r, T)max?

where ħ = 1.05·10-34

J s – Planck’s constant (from the drawing

2) R e?

that); c = 3·108 m/s – speed of light; k = 1.38·10-23

J/K – Boltzmann constant. Let's substitute the numerical values:

6,63 10 34 3 108

3,14 6,63 10 34 3 10

4.82 1015 e 12,

1,38 10 23 2 103 6 107

6 10 7 5

2.96 1010 W

3 107

m2 mm

m2 mm

2). Energy luminosity R e we find from the definition spectral

luminosity density r, T:

Re r, T d r, T d r, T (2 1 ) .

We took into account that the average spectral density of the body's energy luminosity r, T is a constant value and can be taken out of the sign of the integral. Let's substitute the numerical values:

m 2K 4

P = ?

All supplied power will go towards the difference between the radiation of the tungsten filament and the absorption of heat (radiation) from the environment:

P = F e,isl – F e,abs.

We find the radiation (absorption) flux using the formula:

Fe = Re S,

where S =πd ·ℓ – area of ​​the lateral surface of the bottom

ti (cylinder). Then:

P = R e,islS – R e,absorb S = (R e,isl – R e,absorb) S ,

Energetic luminosity (emissivity) R e of the gray body - energy

energy emitted per unit time by a unit surface of a body is proportional to the fourth power of the absolute temperature of the body T4, expressed by the law Stefan-Boltzmann:

R e =a T ·σ ·T 4,

where σ is the Stefan-Boltzmann constant.

Let's substitute it and the area into the power input formula:

Р = (аТ σТ4 – аТ σТ4 okr) πdℓ= аТ σ(Т4 – Т4 okr) πdℓ , Let's substitute the numerical values:

P = 0.3 5.67 10-8 3.14 0.2 5 10-4 = 427.5 W. Answer: P = 427.5 W.

A black thin-walled metal cube with side a = 10 cm is filled with water at temperature T1 = 80°C. Determine the cooling time of the cube to a temperature T 2 = 30°C if it is placed inside a blackened vacuum chamber. The temperature of the chamber walls is maintained close to absolute zero.