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Chapter 1. Electrodynamics
Many physical phenomena observed in nature and the life around us cannot be explained only on the basis of the laws of mechanics, molecular kinetic theory and thermodynamics. These phenomena manifest forces acting between bodies at a distance, and these forces do not depend on the masses of the interacting bodies and, therefore, are not gravitational. These forces are called electromagnetic forces.
The ancient Greeks knew about the existence of electromagnetic forces. But the systematic, quantitative study of physical phenomena in which the electromagnetic interaction of bodies is manifested began only at the end of the 18th century. Through the work of many scientists in the 19th century, the creation of a harmonious science studying electrical and magnetic phenomena was completed. This science, which is one of the most important branches of physics, is called electrodynamics.
The main objects of study in electrodynamics are electric and magnetic fields created by electric charges and currents.
Pendant.
A coulomb is a unit of measurement of electrical charge (amount of electricity) as well as the flux of electrical induction (flux of electrical displacement) in the International System of Units (SI). It has a Russian designation - Kl and an international designation - C.
Pendant as a unit of measurement
Application of the pendant
Representation of a pendant in other units of measurement - formulas
Multiples and submultiples of coulomb units
Interesting examples
Other units of measurement
Examples of static electricity
Thunderstorms on Earth. View from the International Space Station. Photos by NASA.
Since childhood, we have been instinctively afraid of thunder, although in itself it is absolutely safe - just an acoustic consequence of a menacing lightning strike, which is caused by atmospheric static electricity. Sailors from the times of the sailing fleet fell into awe when they observed the lights of St. Elmo on their masts, which are also a manifestation of atmospheric static electricity. People endowed the supreme gods of ancient religions with an integral attribute in the form of lightning, be it the Greek Zeus, the Roman Jupiter, the Scandinavian Thor or the Russian Perun.
Air Canada plane on the ground during refueling
Centuries have passed since people first began to be interested in electricity, and sometimes we do not even suspect that scientists, having drawn thoughtful conclusions from the study of static electricity, are saving us from the horrors of fires and explosions. We've tamed electrostatics by pointing lightning rods at the sky and equipping fuel tankers with grounding devices that allow electrostatic charges to escape safely into the ground. And, nevertheless, static electricity continues to misbehave, interfering with the reception of radio signals - after all, up to 2000 thunderstorms are raging on Earth at the same time, which generate up to 50 lightning strikes every second.
People have been studying static electricity since time immemorial; We even owe the term “electron” to the ancient Greeks, although they meant something slightly different by this - that’s what they called amber, which was perfectly electrified by friction (other - Greek ἤλεκτρον - amber). Unfortunately, the science of static electricity was not without casualties - Russian scientist Georg Wilhelm Richmann was killed by a lightning bolt during an experiment, which is the most dangerous manifestation of atmospheric static electricity.
Static electricity and weather
To a first approximation, the mechanism of formation of charges in a thundercloud is in many ways similar to the mechanism of electrification of a comb - electrification by friction occurs in the same way. Ice floes, formed from small droplets of water, cooled due to transport by rising air currents to the upper, colder part of the cloud, collide with each other. Larger pieces of ice are charged negatively, and smaller pieces are charged positively. Due to the difference in weight, a redistribution of ice floes in the cloud occurs: large, heavier floes fall to the lower part of the cloud, and smaller, lighter floes gather at the top of the thundercloud. Although the cloud as a whole remains neutral, the lower part of the cloud receives a negative charge, and the upper part receives a positive charge.
Franklin on a hundred dollar bill
Just as an electrified comb attracts a balloon by inducing an opposite charge on the side closest to the comb, a thundercloud induces a positive charge on the surface of the Earth. As a thundercloud develops, the charges increase, while the field strength between them increases, and when the field strength exceeds a critical value for the given weather conditions, an electrical breakdown of the air occurs - a lightning discharge.
Trust in God, and don’t forget about the lightning rod!
Humanity is indebted to Benjamin Franklin—later President of the Supreme Executive Council of Pennsylvania and the first Postmaster General of the United States—for the invention of the lightning rod (it would be more accurate to call it a lightning rod), which forever saved the world's population from fires caused by lightning striking buildings. By the way, Franklin did not patent his invention, making it available to all mankind.
Lightning did not always cause only destruction - the Ural ore miners determined the location of iron and copper ores precisely by the frequency of lightning strikes at certain points in the area.
Leyden jars on display at the Canadian Museum of Science and Technology
Among the scientists who devoted their time to studying the phenomena of electrostatics, it is necessary to mention the Englishman Michael Faraday, later one of the founders of electrodynamics, and the Dutchman Pieter van Muschenbrouck, the inventor of the prototype of the electric capacitor - the famous Leyden jar.
Watching DTM, IndyCar or Formula 1 races, we don’t even suspect that mechanics call pilots to change tires to rain tires, relying on weather radar data. And these data, in turn, are based precisely on the electrical characteristics of approaching thunderclouds.
Weather radar at the airport. Pearson, Toronto
Static electricity is our friend and enemy at the same time: radio engineers do not like it when they pull on grounding bracelets when repairing burnt circuit boards as a result of a nearby lightning strike - in this case, as a rule, the input stages of the equipment fail. If grounding equipment is faulty, it can cause severe man-made disasters with tragic consequences - fires and explosions of entire factories.
Static electricity in medicine
However, it comes to the aid of people with heart rhythm disturbances caused by chaotic convulsive contractions of the patient’s heart. Its normal operation is restored by passing a small electrostatic discharge using a device called a defibrillator. The scene of a patient returning from the dead with the help of a defibrillator is a kind of classic for a certain genre of cinema. It should be noted that movies traditionally show a monitor with a missing heartbeat signal and an ominous straight line, when in fact using a defibrillator does not help if the patient's heart has stopped.
The wing dischargers on the Boeing 738-800 are designed to eliminate static electricity to ensure reliable operation of the avionics.
Other examples
It would be useful to remember the need to metallize aircraft to protect against static electricity, that is, to connect all metal parts of the aircraft, including the engine, into one electrically integral structure. Static dischargers are installed at the tips of the entire tail of the aircraft to drain static electricity that accumulates during flight due to air friction against the aircraft body. These measures are necessary to protect against interference caused by static electricity and to ensure reliable operation of the avionics equipment.
Electrostatics plays a certain role in introducing students to the section “Electricity” - perhaps no other section of physics knows more spectacular experiments - here you have hair standing on end, and a balloon chasing a comb, and the mysterious glow of fluorescent lamps without any connection wires! But this glow effect of gas-filled devices saves the lives of electricians dealing with high voltage in modern power lines and distribution networks.
And most importantly, scientists have come to the conclusion that we probably owe the appearance of life on Earth to static electricity, or more precisely to its discharges in the form of lightning. During experiments in the middle of the last century, with the passage of electrical discharges through a mixture of gases, close in composition to the primary composition of the Earth’s atmosphere, one of the amino acids was obtained, which is the “building block” of our life.
Uninterruptible power supplies (UPS) are used to protect equipment from voltage dips, power outages and high voltage pulses in an industrial power supply network that can occur during indirect lightning strikes
To tame electrostatics, it is very important to know the potential difference or electrical voltage, for the measurement of which instruments called voltmeters were invented. The concept of electrical voltage was introduced by the 19th century Italian scientist Alessandro Volta, after whom this unit is named. At one time, galvanometers named after Volta's compatriot Luigi Galvani were used to measure electrostatic voltage. Unfortunately, these electrodynamic type devices introduced distortions into the measurements.
Pendant as a unit of measurement:
A coulomb is a unit of measurement of electrical charge (amount of electricity) as well as flux of electrical induction (flux of electrical displacement) in the International System of Units (SI), named after the French physicist and engineer Charles Coulomb.
The pendant as a unit of measurement has a Russian designation - Kl and an international designation - S.
1 coulomb is defined as the amount of charge passing through a conductor at a current of 1 ampere in 1 second.
Cl = A · s.
1 C = 1 A s = 1/3600 ampere hour.
The charge of one pendant is very large. If two charge carriers (q1 = q2 = 1 C) were placed in a vacuum at a distance of 1 m, then they would interact with a force of 9⋅109 N, that is, with the force with which the Earth’s gravity attracts an object weighing about 1 million tons.
Electric charge (amount of electricity) is a physical scalar quantity. Electric charge carriers are electrically charged elementary particles (electron, positron, proton, etc.). The smallest particle by mass that is stable in a free state and has one negative elementary electric charge is the electron. The electric charge of an electron is indivisible and equal to -1.6021766208(98)⋅10−19 C. The charge of a proton is also equal to the charge of an electron, but with the opposite sign (+ sign) and is equal to +1.6021766208(98)⋅10−19 C.
Thus, the elementary electric charge (to within a sign equal to the charge of an electron or proton) is the above value +/- 1.602176 6208(98)⋅10−19 C. Accordingly, the electric charge of 6.24151⋅1018 electrons is equal to -1 C, and the electric charge of 6.24151⋅1018 protons is equal to +1 C. In this case, the mass of the electron is 9.10938356(11)⋅10−31 kg, and that of the proton is 1.672 621 923 69(51)⋅10−27 kg.
The smallest antiparticle stable in a free state with a positive elementary charge is the positron, which has the same electric charge as the electron, but with a + sign. The electric charge of a positron is +1.6021766208(98)⋅10−19 C. The positron mass is 9.10938356(11)⋅10−31.
The coulomb was introduced into the International System of Units by the decision of the XI General Conference on Weights and Measures in 1960, simultaneously with the adoption of the SI system as a whole. In accordance with the SI rules regarding derived units named after scientists, the name of the unit “coulomb” is written with a lowercase letter, and its designation with a capital letter (Cl). This spelling of the designation is also preserved in the designations of derived units formed using a pendant.
What device measures electric charge?
The device that determines electric charge is called an electroscope.
An electroscope (from the Greek words “electron” and skopeo - to observe, to detect) is a device for indicating the presence of an electric charge.
The operating principle of an electroscope is based on the fact that mutually repulsive forces act on similarly charged bodies.
You can also measure electric charge using an electrometer, in the simplest case consisting of a metal rod and a pointer that can rotate around a horizontal axis
You may ask, how does an electrometer differ from an electroscope? An electroscope and an electrometer are devices for detecting charges. The electrometer has a pointer that also allows you to estimate (measure) the electric charge.
That is, the electroscope finds the charge, and the electrometer also measures the strength of the charge (meter - measure, calculate)
Multiples and submultiples of the coulomb:
Multiples and submultiples are formed using standard SI prefixes.
| Multiples | Dolnye | ||||||
| magnitude | Name | designation | magnitude | Name | designation | ||
| 101 Kl | deca pendant | yesCl | daC | 10−1 Cl | decicoulone | dCL | dC |
| 102 Kl | hectocoulomb | gC | hC | 10−2 Cl | centicoulomb | sKl | cC |
| 103 Kl | kilocoulomb | kCl | kC | 10−3 Cl | milliculomb | mC | mC |
| 106 Kl | mega pendant | MCL | M.C. | 10−6 Cl | microcoulomb | µC | µC |
| 109 Kl | gigakulon | GKl | G.C. | 10−9 Cl | nanocoulomb | nCl | nC |
| 1012 Cl | terakulon | TKl | TC | 10−12 Cl | picoculomb | pCL | pC |
| 1015 Kl | petacoulomb | Pcl | PC | 10−15 Kl | femtocoulomb | fkl | fC |
| 1018 Kl | exaculon | ECL | E.C. | 10−18 Cl | attocoulomb | aKl | aC |
| 1021 Kl | zettacoulomb | ZKl | ZC | 10−21 Cl | zeptoculone | zkl | zC |
| 1024 Kl | iottakulon | ICL | YC | 10−24 Cl | ioctocoulomb | iKl | yC |
Basic electrical quantities
- home
- Measuring instruments
Let's consider the basic electrical quantities that we study first at school, then in secondary and higher educational institutions. For convenience, we will summarize all the data in a small table. Definitions of individual quantities will be given after the table in case of any misunderstandings.
| Magnitude | SI unit | Name of electrical quantity |
| q | Kl - pendant | charge |
| R | Om - om | resistance |
| U | V – volt | voltage |
| I | A – ampere | Current strength (electric current) |
| C | F – farad | Capacity |
| L | Mr. Henry | Inductance |
| sigma | CM - Siemens | Electrical conductivity |
| e0 | 8.85418781762039*10-12 f/m | Electrical constant |
| φ | V – volt | Electric field point potential |
| P | W – watt | Active power |
| Q | VAR – volt-ampere-reactive | Reactive power |
| S | Va – volt-ampere | Full power |
| f | Hz - hertz | Frequency |
There are decimal prefixes that are used in the name of the quantity and serve to simplify the description. The most common of them are: mega, miles, kilo, nano, pico. The table shows other prefixes, except those mentioned.
| Decimal multiplier | Pronunciation | Designation (Russian/international) |
| 10-30 | cuecto | q |
| 10-27 | ronto | r |
| 10-24 | iocto | and/y |
| 10-21 | zepto | s/z |
| 10-18 | atto | a |
| 10-15 | femto | f/f |
| 10-12 | pico | p/p |
| 10-9 | nano | n/n |
| 10-6 | micro | μ/μ |
| 10-3 | Milli | m/m |
| 10-2 | centi | c |
| 10-1 | deci | d/d |
| 101 | soundboard | yes/da |
| 102 | hecto | g/h |
| 103 | kilo | k/k |
| 106 | mega | M |
| 109 | giga | G/G |
| 1012 | tera | T |
| 1015 | peta | P/P |
| 1018 | exa | E/E |
| 1021 | zeta | Z/Z |
| 1024 | yotta | Y/Y |
| 1027 | Ronna | R |
| 1030 | quecca | Q |
The strength of an electric current of 1A is a value equal to the ratio of a charge of 1 C passing through a surface (conductor) in 1 s of time to the time of passage of the charge through the surface. For current to flow, the circuit must be closed.
Current strength is measured in amperes. 1A=1Kl/1c
In practice there are
1kA = 1000A
1mA = 0.001A
1uA = 0.000001A
Electric voltage is the potential difference between two points in an electric field. The magnitude of electrical potential is measured in volts, therefore voltage is measured in volts (V).
1 Volt is the voltage that is necessary to release 1 Watt of energy in a conductor when a current of 1 Ampere flows through it.
The unit of electric current voltage is the following ratio: 1V=1W/1A.
In practice, the following variants of units of measurement of electric potential, or rather potential difference, are encountered:
- 1kV = 1000V
- 1mV = 0.001V
Electrical resistance is the characteristic of a conductor that prevents electric current from flowing through it. It is defined as the ratio of the voltage at the ends of the conductor to the current in it. Measured in ohms (ohms). Within certain limits the value is constant.
1 Ohm is the resistance of a conductor when a direct current of 1A flows through it and a voltage of 1V arises at the ends.
From the school physics course we all remember the formula for a homogeneous conductor of constant cross-section:
R=ρlS – the resistance of such a conductor depends on the cross-section S and length l
where ρ is the resistivity of the conductor material, tabular value.
Between the three quantities described above, Ohm's law exists for a DC circuit.
The current in the circuit is directly proportional to the voltage in the circuit and inversely proportional to the resistance of the circuit - Ohm's law.
I=U/R
Electrical capacitance is the ability of a conductor to accumulate electrical charge.
Capacitance is measured in farads (1F).
1F = 1Kl/1V
1F is the capacitance of a capacitor between the plates of which a voltage of 1V occurs when charged at 1C.
In practice there are
1pF = 0.000000000001F
1nF = 0.000000001F
Inductance is a quantity that characterizes the ability of a circuit through which electric current flows to create and accumulate a magnetic field.
Inductance is measured in henries.
1Gn = (V*s)/A
1H is a value equal to the self-inductive emf that occurs when the current in the circuit changes by 1A within 1 second.
In practice there are
1mH = 0.001H
Electrical conductivity is a value indicating the ability of a body to conduct electric current. Reciprocal of resistance.
Electrical conductivity is measured in siemens.
1cm = Ohm-1
How to choose a shunt for an ammeter
How to connect a pointer ammeter
