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The original site "Cool Physics" (class-fizika.narod.ru) has been included in the catalog releases since 2006 “Educational Internet resources for basic general and secondary (complete) general education”, approved by the Ministry of Education and Science of the Russian Federation, Moscow.
Read, learn, explore!
The world of physics is interesting and fascinating, it invites all the curious to take a journey through the pages of the Cool Physics website.
And for starters - a visual map of physics that shows where they originate and how they are connected to each other various areas physicists, what they study, and what they are needed for.
The Map of Physics was created based on the video The Map of Physics by Dominic Willimman on the Domain of Science channel.
Physics and the secrets of artists
The secrets of the mummies of the pharaohs and the inventions of Rebrandt, forgeries of masterpieces and the secrets of papyri Ancient Egypt- art hides many secrets, but modern physicists With the help of new methods and instruments, explanations are found for everything more amazing secrets of the past......... read
ABC of physics
Almighty friction
It is everywhere, but where can you go without it?
But here are three hero assistants: graphite, molybdenite and Teflon. These amazing substances, having very high particle mobility, are currently used as an excellent solid lubricant......... read
Aeronautics
"So they rise to the stars!" - inscribed on the coat of arms of the founders of aeronautics, the Montgolfier brothers.
Famous writer Jules Verne flew hot air balloon only 24 minutes, but it helped him create the most fascinating works of art......... read
Steam engines
“This mighty giant was three meters tall: the giant easily pulled a van with five passengers. On the head of the Steam Man there was a chimney pipe from which thick black smoke was pouring out... everything, even his face, was made of iron, and all of it was constantly grinding and rumbled..." Who is this about? Who are these praises for? ......... read
Secrets of the magnet
Thales of Miletus endowed him with a soul, Plato compared him to a poet, Orpheus found him like a groom... During the Renaissance, a magnet was considered a reflection of the sky and was credited with the ability to bend space. The Japanese believed that a magnet is a force that will help turn fortune towards you......... read
On the other side of the mirror
Do you know how much interesting discoveries can give a “through the looking glass”? The image of your face in the mirror has its right and left halves swapped. But faces are rarely completely symmetrical, so others see you completely differently. Have you thought about this? ......... read
Secrets of the common top
“The realization that the miraculous was near us comes too late.” - A. Blok.
Did you know that the Malays can watch the spinning top in fascination for hours? However, considerable skill is required to spin it correctly, because the weight of a Malayan top can reach several kilograms......... read
Inventions of Leonardo da Vinci
“I want to create miracles!” he said and asked himself: “But tell me, have you done anything?” Leonardo da Vinci wrote his treatises in secret writing using an ordinary mirror, so his encrypted manuscripts could be read for the first time only three centuries later.........
For uniformly accelerated motion, the following are true: following equations, which we present without output:
As you understand, vector formula on the left and two scalar formulas on the right are equal. From the point of view of algebra, scalar formulas mean that with uniformly accelerated motion the displacement projections depend on time along quadratic law. Compare this with the nature of projections instantaneous speed(see § 12-h).
Knowing that sx = x – xo and sy = y – yo (see § 12), from the two scalar formulas from the upper right column we obtain equations for the coordinates:
Since the acceleration during uniformly accelerated motion of a body is constant, the coordinate axes can always be positioned so that the acceleration vector is directed parallel to one axis, for example the Y axis. Consequently, the equation of motion along the X axis will be noticeably simplified:
x = xo + υox t + (0) and y = yo + υoy t + ½ ay t²
Please note that the left equation coincides with the equation of uniform rectilinear motion (see § 12-g). This means that uniformly accelerated motion can “compose” from uniform motion along one axis and uniformly accelerated motion along the other. This is confirmed by the experience with the core on a yacht (see § 12-b).
Task. Stretching out her arms, the girl tossed the ball. He rose 80 cm and soon fell at the girl’s feet, flying 180 cm. At what speed was the ball thrown and what speed did the ball have when it hit the ground?
Let us square both sides of the equation for the projection of instantaneous velocity onto the Y axis: υy = υoy + ay t (see § 12). We get the equality:
υy² = ( υoy + ay t )² = υoy² + 2 υoy ay t + ay² t²
Let’s take the factor 2 ay out of brackets only for the two right-hand terms:
υy² = υoy² + 2 ay ( υoy t + ½ ay t² )
Note that in brackets we get the formula for calculating the displacement projection: sy = υoy t + ½ ay t². Replacing it with sy, we get:
Solution. Let's make a drawing: direct the Y axis upward, and place the origin of coordinates on the ground at the girl's feet. Let us apply the formula we derived for the square of the velocity projection, first at the top point of the ball’s rise:
0 = υoy² + 2·(–g)·(+h) ⇒ υoy = ±√¯2gh = +4 m/s
Then, when starting to move from the top point down:
υy² = 0 + 2·(–g)·(–H) ⇒ υy = ±√¯2gh = –6 m/s
Answer: the ball was thrown upward with a speed of 4 m/s, and at the moment of landing it had a speed of 6 m/s, directed against the Y axis.
Note. We hope you understand that the formula for the squared projection of instantaneous velocity will be correct by analogy for the X axis:
If the movement is one-dimensional, that is, it occurs only along one axis, you can use either of the two formulas in the framework.
The position of bodies relative to the selected coordinate system is usually characterized by a radius vector depending on time. Then the position of the body in space at any time can be found using the formula:
.
(Recall that this is the main task of mechanics.)
Among the many various types the simplest movement is uniform– movement at a constant speed (zero acceleration), and the velocity vector () must remain unchanged. Obviously, such a movement can only be rectilinear. Precisely when uniform motion the movement is calculated by the formula:
Sometimes the body moves curvilinear trajectory so that the velocity module remains constant () (such movement cannot be called uniform and the formula cannot be applied to it). In this case distance traveled can be calculated using a simple formula:
An example of such a movement is movement in a circle with a constant absolute speed.
More difficult is uniformly accelerated motion– movement with constant acceleration(). For such a movement, two kinematic formulas are valid:
from which two additional formulas can be obtained, which can often be useful in solving problems:
;
Uniformly accelerated motion doesn't have to be straightforward. It is only necessary that vector acceleration remained constant. An example of uniformly accelerated, but not always rectilinear motion is motion with acceleration free fall (g= 9.81 m/s 2), directed vertically downwards.
From school course physics is familiar and more complex movement – harmonic vibrations a pendulum for which the formulas are not valid.
At movement of a body in a circle with a constant absolute speed it moves with the so-called normal (centripetal) acceleration
directed towards the center of the circle and perpendicular to the speed of movement.
In more general case motion along a curvilinear trajectory with varying speed, the acceleration of a body can be decomposed into two mutually perpendicular components and presented as the sum of tangential (tangent) and normal (perpendicular, centripetal) acceleration:
,
where is the unit vector of the velocity vector and the unit unit normal to the trajectory; R– radius of curvature of the trajectory.
The motion of bodies is always described relative to some reference system (FR). When solving problems, it is necessary to choose the most convenient SO. For progressively moving COs, the formula is
allows you to easily move from one CO to another. In the formula – the speed of the body relative to one CO; – body speed relative to the second reference point; – speed of the second CO relative to the first.
Self-test questions and tasks
1) Model material point: what is its essence and meaning?
2) Formulate the definition of uniform, uniformly accelerated motion.
3) Formulate the definitions of the basic kinematic quantities (radius vector, displacement, speed, acceleration, tangential and normal acceleration).
4) Write the formulas for the kinematics of uniformly accelerated motion and derive them.
5) Formulate Galileo’s principle of relativity.
2.1.1. Straight-line movement
Problem 22.(1) A car moves along a straight section of road at a constant speed of 90. Find the displacement of the car in 3.3 minutes and its position at the same moment in time, if at the initial moment of time the car was at a point whose coordinate is 12.23 km and the axis Ox directed 1) along the movement of the car; 2) against the movement of the car.
Problem 23.(1) A cyclist moves along a country road to the north at a speed of 12 for 8.5 minutes, then he turns right at the intersection and travels another 4.5 km. Find the displacement of the cyclist during his movement.
Problem 24.(1) A skater moves in a straight line with an acceleration of 2.6, and in 5.3 s his speed increases to 18. Find initial value speed skater speed. How far will the athlete run during this time?
Problem 25.(1) The car moves in a straight line, slowing down in front of a speed limit sign of 40 with an acceleration of 2.3 How long did this movement last if before braking the car’s speed was 70? At what distance from the sign did the driver start to brake?
Problem 26.(1) With what acceleration is the train moving if its speed increases from 10 to 20 along a journey of 1200 m? How long did the train take on this journey?
Problem 27.(1) A body thrown vertically upward returns to the ground after 3 s. What was the initial speed of the body? What is the maximum height it has been to?
Problem 28.(2) A body on a rope is lifted from the surface of the earth with an acceleration of 2.7 m/s 2 vertically upward from a state of rest. After 5.8 s the rope broke. How long did it take the body to reach the ground after the rope broke? Neglect air resistance.
Problem 29.(2) The body begins to move without an initial speed with an acceleration of 2.4 Determine the path traveled by the body in the first 16 s from the beginning of the movement, and the path traveled over the next 16 s. From what average speed did the body move during these 32 s?
2.1.2. Uniformly accelerated motion in a plane
Problem 30.(1) A basketball player throws a ball into a hoop at a speed of 8.5 at an angle of 63° to the horizontal. At what speed did the ball hit the hoop if it reached it in 0.93 s?
Problem 31.(1) A basketball player throws the ball into the hoop. At the moment of the throw, the ball is at a height of 2.05 m, and after 0.88 s it falls into the ring located at a height of 3.05 m. From what distance from the ring (horizontally) was the throw made if the ball was thrown at an angle of 56 o to the horizon?
Problem 32.(2) The ball is thrown horizontally with a speed of 13, after some time its speed turns out to be equal to 18. Find the movement of the ball during this time. Neglect air resistance.
Problem 33.(2) A body is thrown at a certain angle to the horizon with an initial speed of 17 m/s. Find the value of this angle if the body’s flight range is 4.3 times greater than the maximum lift height.
Problem 34.(2) A bomber diving at a speed of 360 km/h drops a bomb from a height of 430 m, being horizontally at a distance of 250 m from the target. At what angle should a bomber dive? At what height will the bomb be 2 seconds after the start of its fall? What speed will it have at this point?
Problem 35.(2) An airplane flying at an altitude of 2940 m at a speed of 410 km/h dropped a bomb. How long before passing over the target and at what distance from it must the plane release the bomb in order to hit the target? Find the magnitude and direction of the bomb’s velocity after 8.5 s from the beginning of its fall. Neglect air resistance.
Problem 36.(2) A projectile fired at an angle of 36.6 degrees to the horizontal was at the same height twice: 13 and 66 seconds after departure. Determine the initial speed, maximum height lift and range of the projectile. Neglect air resistance.
2.1.3. Circular movement
Problem 37.(2) A sinker moving on a line in a circle with constant tangential acceleration, by the end of the eighth revolution it had a speed of 6.4 m/s, and after 30 seconds of movement its normal acceleration became 92 m/s 2 . Find the radius of this circle.
Problem 38.(2) A boy riding on a carousel moves when the carousel stops along a circle with a radius of 9.5 m and covers a path of 8.8 m, having a speed of 3.6 m/s at the beginning of this arc and 1.4 m/s at the end. With. Determine the total acceleration of the boy at the beginning and end of the arc, as well as the time of his movement along this arc.
Problem 39.(2) A fly sitting on the edge of a fan blade, when it is turned on, moves in a circle of radius 32 cm with a constant tangential acceleration of 4.6 cm/s 2 . How long after the start of motion will the normal acceleration be twice as large as the tangential acceleration and what will it be equal to? linear speed flies at this point in time? How many revolutions will the fly make during this time?
Problem 40.(2) When the door is opened, the handle moves from rest in a circle of radius 68 cm with a constant tangential acceleration equal to 0.32 m/s 2 . Find dependency full acceleration pens from time to time.
Problem 41.(3) To save space, the entrance to one of the highest bridges in Japan is arranged in the form of a helical line wrapping around a cylinder with a radius of 65 m. The road surface is about horizontal plane angle 4.8 o. Find the acceleration of a car moving along this road at a constant absolute speed of 85 km/h?
2.1.4. Relativity of motion
Problem 42.(2) Two ships are moving relative to the shores at a speed of 9.00 and 12.0 knots (1 knot = 0.514 m/s), directed at an angle of 30 and 60 o to the meridian, respectively. At what speed is the second ship moving relative to the first?
Problem 43.(3) A boy who can swim at a speed 2.5 times slower than the speed of the river current wants to swim across this river so that he is carried downstream as little as possible. At what angle to the shore should the boy swim? How far will it be carried if the width of the river is 190 m?
Problem 44.(3) Two bodies simultaneously begin to move from one point in the gravity field with the same speed equal to 2.6 m/s. The speed of one body is directed at an angle π/4, and the other – at an angle –π/4 to the horizon. Define relative speed of these bodies 2.9 s after the start of their movement.
Kinematics is the study of classical mechanical motion in physics. Unlike dynamics, science studies why bodies move. She answers the question of how they do it. In this article we will look at what acceleration and motion with constant acceleration are.
The concept of acceleration
When a body moves in space, over a period of time it covers a certain path, which is the length of the trajectory. To calculate this path, we use the concepts of speed and acceleration.
Speed as physical quantity characterizes the rate of change in time of the distance traveled. The speed is directed tangentially to the trajectory in the direction of the body movement.
Acceleration is a slightly more complex quantity. In short, it describes the change in speed at a given point in time. The math looks like this:
To understand this formula more clearly, let's give a simple example: suppose that in 1 second of movement the speed of the body increased by 1 m/s. These numbers, substituted into the expression above, lead to the result: the acceleration of the body during this second was equal to 1 m/s 2 .
The direction of acceleration is completely independent of the direction of velocity. Its vector coincides with the vector of the resulting force that causes this acceleration.
It should be noted important point in the given definition of acceleration. This value characterizes not only the change in speed in magnitude, but also in direction. Last fact should be taken into account in case curvilinear movement. Further in the article we will only consider rectilinear movement.
Speed when moving with constant acceleration
Acceleration is constant if it maintains its magnitude and direction during movement. Such motion is called uniformly accelerated or uniformly decelerated - it all depends on whether acceleration leads to an increase in speed or to a decrease in speed.
In the case of a body moving with constant acceleration, the speed can be determined by one of following formulas:
The first two equations characterize uniformly accelerated movement. The difference between them is that the second expression is applicable for the case of non-zero initial velocity.
The third equation is an expression for the speed of uniformly slow motion with constant acceleration. Acceleration is directed against speed.
The graphs of all three functions v(t) are straight lines. In the first two cases, the straight lines have a positive slope relative to the x-axis; in the third case, this slope is negative.
Formulas for the distance traveled
For a path in the case of motion with constant acceleration (acceleration a = const), it is not difficult to obtain formulas if you calculate the integral of the speed over time. Having done this mathematical operation for the three equations written above, we obtain the following expressions for the path L:
L = v 0 *t + a*t 2 /2;
L = v 0 *t - a*t 2 /2.
The graphs of all three path functions versus time are parabolas. In the first two cases, the right branch of the parabola increases, and for the third function it gradually reaches a certain constant, which corresponds to the distance traveled until the body stops completely.
Problem solution
Moving at a speed of 30 km/h, the car began to accelerate. In 30 seconds he covered a distance of 600 meters. What was the acceleration of the car?
First of all, let's convert the initial speed from km/h to m/s:
v 0 = 30 km/h = 30000/3600 = 8.333 m/s.
Now let's write the equation of motion:
L = v 0 *t + a*t 2 /2.
From this equality we express the acceleration, we get:
a = 2*(L - v 0 *t)/t 2 .
All physical quantities in this equation are known from the problem conditions. We substitute them into the formula and get the answer: a ≈ 0.78 m/s 2 . Thus, moving with constant acceleration, the car increased its speed by 0.78 m/s every second.
Let us also calculate (for interest) what speed he acquired after 30 seconds of accelerated movement, we get:
v = v 0 + a*t = 8.333 + 0.78*30 = 31.733 m/s.
The resulting speed is 114.2 km/h.
ABSTRACT
Lectures on physics
MECHANICS
Kinematics
Kinematics is a branch of mechanics that studies mechanical movement without analyzing the reasons causing it.
Mechanical movement- simplest form movement of bodies, which consists in changing over time the position of some bodies relative to others, or the position of parts of the body relative to each other. In this case, the bodies interact according to the laws of mechanics.
Basic Concepts:
Material point- a body whose size and shape can be neglected.
Reference body– the body relative to which the movement of the body under study (other bodies) is considered.
Frame of reference– a set of a reference body, a coordinate system associated with it and a clock stationary relative to the reference body.
Radius Vect op – vector connecting the origin of coordinates with the point of location of the body in at the moment time.
Trajectory– the line that the body describes ( center of mass) during its movement,
Path – scalar physical quantity, equal to length trajectory described by the body over the considered period of time. ( , m)
Speed– vector physical quantity characterizing the speed of movement of a particle along a trajectory, and the direction in which the particle moves at each moment of time, i.e. changes in position over time (υ, m/s).
Acceleration – vector physical quantity, equal to the ratio body speed increments per some period of time to the size of this gap, i.e. speed (rate) of speed change ( A, m/s 2).
The acceleration vector can change by changing its direction, magnitude, or both. If the speed decreases, then the term “deceleration” is used.
Point speed
Types of movements:
movement of a body in which it travels identical paths in any equal intervals of time.
1 – Coordinate of the point at the moment of time t.
2 – Point coordinate in initial moment time t= 0
3 – Projection of the velocity vector onto coordinate axis
Motion with constant acceleration
a= = S = υ 0 t ± υ = υ 0 ± a t
Uniform movement around a circle -
Dynamics
Dynamics - a branch of mechanics that studies causes emergence mechanical movement.
Weight– scalar physical quantity, which is a quantitative measure of the inertia of a body, and also characterizes the amount of substance (m, kg),
Strength– a vector physical quantity that is a measure of the interaction of bodies and leads to the appearance of acceleration in the body or to deformation of the body. Force is characterized by magnitude, direction and point of application (F, N).
FORCES
Newton's laws:
Newton's first law:
in inertial reference systems closed system continues to remain in a state of rest or rectilinear uniform motion.
Classical mechanics Newton is applicable in a special class inertial reference systems.
All inertial systems references move relative to each other rectilinearly and uniformly.
Newton's second law:
a force acting on a system from outside leads to acceleration of the system.
Newton's third law:
the action force is equal in magnitude and opposite in direction to the reaction force; the forces have the same nature, but are applied to different bodies and are not compensated.
Forces in nature:
Law of conservation of momentum
Momentum is a vector physical quantity, equal to the product body weight to its speed: ,
Law of conservation of momentum:
Law of Conservation of Energy
Energy– characteristics of the movement and interaction of bodies, their ability to make changes in outside world(E, J).
Total mechanical energy is understood as the sum of kinetic and potential energies:
Total mechanical energy
Kinetic energy
Body potential energy- a scalar physical quantity that characterizes the ability of a body (or a material point) to do work due to its presence in the field of action of forces.
Body kinetic energy- the energy of a mechanical system, depending on the speed of movement of its points.
Conservation Law mechanical energy:
Absolute scale temperatures
English introduced physicist W. Kelvin
- no negative temperatures
SI unit of absolute temperature: [T] = 1K (Kelvin)
Zero temperature absolute scale is absolute zero(0K = -273 C), the most low temperature in nature. Currently, the lowest temperature has been reached - 0.0001K.
In magnitude, 1K is equal to 1 degree on the Celsius scale.
Relationship between the absolute scale and the Celsius scale: in formulas absolute temperature is denoted by the letter "T", and temperature on the Celsius scale by the letter "t".
Basic equation of MKT gas
The basic MKT equation connects the microparameters of particles (the mass of a molecule, the average kinetic energy of molecules, the average square of the speed of molecules) with the macroparameters of a gas (p - pressure, V - volume, T - temperature).
average kinetic energy forward movement molecules root mean square speed
average kinetic energy of translational motion of molecules
RMS speed: =
Internal energy of a monatomic ideal gas : U = = pV
Gases are characterized by complete disorder in the arrangement and movement of molecules.
The distance between gas molecules is many times more sizes molecules. Small attractive forces cannot keep molecules close to each other, so gases can expand without limit.
The gas pressure on the walls of the vessel is created by the impacts of moving gas molecules.
Liquid
The thermal motion of molecules in a liquid is expressed by vibrations around the position stable equilibrium within the volume provided to the molecule by its neighbors.
Molecules cannot move freely throughout the entire volume of a substance, but transitions of molecules to neighboring places are possible. This explains the fluidity of the liquid and the ability to change its shape.
In a liquid, the distance between molecules is approximately equal to the diameter of the molecule. When the distance between molecules decreases (compression of the liquid), the repulsive forces increase sharply, so liquids are incompressible.
The thermal motion of molecules in a solid is expressed only by vibrations of particles (atoms, molecules) around a stable equilibrium position.
Most solids have a spatially ordered arrangement of particles that form a regular crystal lattice. Particles of matter (atoms, molecules, ions) are located at vertices - nodes crystal lattice. The nodes of the crystal lattice coincide with the position of stable equilibrium of the particles.
Humidity:
Dew point– temperature at which steam becomes saturated
Solid
Fundamentals of Thermodynamics
Basic concepts:
Thermodynamics– a theory of physics that studies thermal properties macroscopic systems, without referring to the microscopic structure of the bodies that make up the system.
Thermodynamic system– physical system, consisting of large number particles (atoms and molecules) that undergo thermal motion and interact with each other and exchange energies.
Thermodynamics considers only equilibrium states.
Equilibrium states – states in which the parameters thermodynamic system do not change over time.
Thermodynamic process– transition of the system from the initial state to the final state through a sequence of intermediate states (any change in the thermodynamic system).
Thermodynamic processes
Internal energy– energy consisting of the sum of energies molecular interactions and the energy of thermal motion of molecules, depending only on the thermodynamic state of the system.
Ways to change internal energy :
- Commitment mechanical work.
- Heat exchange (heat transfer)
Heat exchange– transfer of internal energies from one body to another.
Heat exchange
desublimation
sublimation
vaporization
condensation
crystallization
melting
Amount of heat (Q, J)– measure of energy
Amount of heat:
First law of thermodynamics
Statement of the first law of thermodynamics:
Getting the job done
Q 2 – energy transferred (the “remainder” of energy is transferred)
The heat engine must operate cyclically. At the end of the cycle, the body returns to its original state, and the internal energy takes on its initial value. The work of the cycle can only be accomplished by external sources, supplying heat to the working fluid.
Real heat engines operate in an open cycle, i.e. after expansion, the gas is released, and a new portion of gas is introduced into the machine.
Coefficient useful action
Efficiency ( η ) – work relation A accomplished by the working fluid per cycle, to the amount of heat Q the resulting working fluid for the same cycle.
η = · 100% = · 100% = · 100%
Efficiency characterizes the degree of efficiency of a heat engine and depends only on the temperature of the heater and refrigerator.
ü For increasing efficiency With a heat engine, you can increase the temperature of the heater and decrease the temperature of the refrigerator;
ü Efficiency is always< 1
Second law of thermodynamics
The second law of thermodynamics determines the direction of processes occurring in nature and associated with the transformation of energy.
Statements of the second law of thermodynamics:
- A thermodynamic process is impossible, as a result of which heat would be transferred from a cold body to a hotter one, without any other changes in nature.
- A process is not possible in nature, the only result of which is the conversion of all the heat received from a certain body into work.
The second law of thermodynamics denies the possibility of using the internal energy reserves of any source without transferring it to more low level, i.e. no refrigerator.
FUNDAMENTALS OF ELECTRODYNAMICS
Electrodynamics- science of properties electromagnetic field.
1. ELECTROSTATICS
- a branch of electrodynamics that studies electrically charged bodies at rest.
Elementary particles may have email charge, then they are called charged; interact with each other with forces that depend on the distance between the particles, but exceed many times the forces of mutual gravity (this interaction is called electromagnetic).
Electric charge
– the main scalar physical quantity that determines the intensity electromagnetic interactions(q, Cl).
1 C - charge passing through in 1 second cross section conductor at a current of 1 A.
There are 2 signs of electric charges: positive and negative.
Particles with like charges repel, and particles with unlike charges attract.
A proton has a positive charge, an electron has a negative charge, and a neutron is electrically neutral.
Elementary charge- a minimum charge that cannot be divided.
Body is charged, if it has an excess of charges of any sign:
negatively charged - if there is an excess of electrons;
positively charged - if there is a lack of electrons.
Electrification of bodies
- one of the ways to obtain charged bodies.
In this case, both bodies are charged, and the charges are opposite in sign, but equal in magnitude.
MAGNETS
Magnets have two poles: S (southern) and N (northern), which have greatest strength attraction.
Like poles of a magnet repel each other, and opposite poles attract.
Magnetic field characteristics:
Magnetic flux(F, Wb) – the number of magnetic induction lines penetrating the site.
Magnetic field strength(N, A/m) – a quantity that characterizes the magnetic field at any point in space created by macrocurrents (currents flowing in the wires of an electrical circuit) in conductors, regardless of environment.
B = μ s N
For rectilinear current: N = ;
in the center circular current: N = ;
in the center of the solenoid: H = .
Magnetic permeability of a substance
The value of magnetic induction depends on the environment in which the magnetic field exists. The ratio of magnetic induction B in a field in a given environment to magnetic induction B o in a vacuum characterizes magnetic properties given environment and is called the relative magnetic permeability of the substance - µ.
ELECTROMAGNETIC INDUCTION
Methods for obtaining induction current:
Phenomenon electromagnetic induction – emergence electric current in a closed conducting loop, which is either at rest in a time-varying magnetic field or moves in a constant magnetic field so that the number of magnetic induction lines penetrating the loop changes. The faster the number of magnetic induction lines changes, the greater the induced current.
LAW OF ELECTROMAGNETIC INDUCTION:
Electric current in a circuit is possible if free charges outside forces act on the conductor. The work of these forces to move a unit positive charge along a closed loop is called emf. When changing magnetic flux through the surface limited by the contour, external forces appear in the contour, the action of which is characterized by induced emf.
Considering the direction of the induction current, according to Lenz's rule:
The induced emf in a closed loop is equal to the rate of change of the magnetic flux through the surface bounded by the loop, taken with the opposite sign.
VORTEX ELECTRIC FIELD
The reason for the occurrence of electric current in a stationary conductor is the electric field.
Any change in the magnetic field generates an inductive electric field, regardless of the presence or absence of a closed circuit, and if the conductor is open, then a potential difference arises at its ends; If the conductor is closed, then an induced current is observed in it.
Eddy currents:
Induction currents in massive conductors are called Foucault currents. Foucauldian currents can reach very large values, because The resistance of massive conductors is low. Therefore, transformer cores are made from insulated plates.
In ferrites - magnetic insulators eddy currents practically do not arise.
Usage eddy currents
Heating and melting of metals in a vacuum, dampers in electrical measuring instruments.
Harmful effect eddy currents
These are energy losses in the cores of transformers and generators due to the release large quantity heat.
SELF-INDUCTION
Self-induction phenomenon– the occurrence of induced emf in a circuit, which is caused by a change in the magnetic field of the current flowing in the same circuit.
Self-magnetic field in a circuit DC changes at the moments of closing and opening the circuit and when the current strength changes.
Inductance
(self-induction coefficient) – a physical quantity showing the dependence Self-induced emf on the size and shape of the conductor and on the environment in which the conductor is located.
The inductance of the coil depends on:
the number of turns, the size and shape of the coil and the relative magnetic permeability of the medium (possibly a core).
ENERGY OF THE MAGNETIC FIELD OF CURRENT
Around a conductor carrying current there is a magnetic field that has energy.
The energy of the magnetic field is equal to the intrinsic energy of the current.
The self-energy of the current is numerically equal to the work that the current source must do to overcome the self-induction emf in order to create a current in the circuit.
AC
AC– current changing in direction and magnitude along harmonic law.
RMS current value- the strength of a direct current that releases the same amount of heat in a conductor during the same time as an alternating current. I =
The instantaneous current value is proportional to the instantaneous voltage value and is in phase: i = = I m cos ωt
The effective value of alternating voltage is determined similarly to the effective value of current U =
The instantaneous voltage value changes according to the harmonic law: u = U m cos ωt
Active resistances– electrical devices that convert electrical energy into internal energy (high-resistance wires, heating coils, resistors).
Power AC.
When the phases of current and voltage oscillations coincide, the instantaneous power of alternating current is equal to:
p = iu = i 2 R= I m U m cos 2ωt
The average power value over an alternating current period is: p =
Inductance and capacitance in an AC circuit:
1. Inductance
In a coil connected to an alternating voltage circuit, the current strength is less than the current strength in the circuit DC voltage for the same coil. Consequently, the coil in an alternating voltage circuit creates more resistance than in a direct voltage circuit.
Voltage leads current in phase by π/2
The inductive reactance is : X L = ωL = 2πνL
Ohm's Law: I m = , where Lω is inductive reactance.
2. Capacity
When a capacitor is connected to a DC voltage circuit, the current is zero, and when a capacitor is connected to an AC voltage circuit, the current is not zero. Therefore, a capacitor in an AC voltage circuit creates less resistance than in a DC circuit.
Capacitance is equal to: X C = =
Resonance in an electrical circuit.
Resonance in an electrical circuit - a phenomenon sharp increase amplitudes forced oscillations current when the frequencies coincide ω 0 = ω, where ω 0 is the natural frequency of the oscillatory circuit, ω is the frequency of the supply voltage.
The operating principle is based on the phenomenon of electromagnetic induction.
The principle of operation at idle speed, i.e. without R n:
ε ind1/ε ind2= ω 1 /ω 2 = k, where ε ind1 And ε ind2– induced emf in the windings, ω 1 and ω 2 - the number of turns in the windings,
k – transformation coefficient.
If k > 1 , then the transformer steps down the voltage; If k< 1 , then the transformer increases the voltage. When idling, the transformer consumes a small amount of energy from the network, which is spent on reversing the magnetization of its core.
Transformers for converting high-power alternating currents have high efficiency.
Broadcast electrical energy:
5. Electromagnetic oscillations and waves
Oscillatory circuit- a circuit in which energy electric field could be converted into magnetic field energy and back.
Electric oscillatory circuit - a system consisting of a capacitor and a coil connected to each other in a closed loop electrical circuit
Available electromagnetic vibrations – periodically repeating changes in current in the coil and voltage between the capacitor plates without consuming energy from external sources.
If the contour is “ideal”, i.e. electrical resistance equals 0 X L = X C ω =
T = 2π – Thomson formula (period of free electromagnetic oscillations in electrical circuit)
Electromagnetic field – special shape matter, a set of electric and magnetic fields.
Alternating electric and magnetic fields exist simultaneously and form a single electromagnetic field.
ü At the charging speed, equal to zero, there is only an electric field.
ü When constant speed charge creates an electromagnetic field.
ü With the accelerated movement of a charge, an electromagnetic wave is emitted, which propagates in space at a finite speed.
Materiality of the electromagnetic field:
ü you can register
ü exists independently of our will and desires
ü has a high but finite speed
Electromagnetic waves
An electromagnetic field varying in time and propagating in space (vacuum) at a speed of 3 × 10 8 m/s forms an electromagnetic wave. The finite speed of propagation of the electromagnetic field leads to the fact that electromagnetic oscillations in space propagate in the form of waves.
Far from the antenna, the values of vectors E and B are in phase.
The main condition for the occurrence of an electromagnetic wave is the accelerated movement of electric charges.
Electromagnetic wave speed: υ = νλ λ = = υ2π
Wave properties:
Ø reflection, refraction, interference, diffraction, polarization;
Ø pressure on the substance;
Ø absorption by the environment;
Ø final speed propagation in vacuum With;
Ø causes the phenomenon of photoelectric effect;
Ø the speed in the medium decreases.
6. WAVE OPTICS
Optics- branch of physics that studies light phenomena.
By modern ideas light has a dual nature (wave-particle duality): light has wave properties and represents electromagnetic waves, but at the same time it is also a flow of particles – photons. Depending on the light range, they appear in to a greater extent certain properties.
Speed of light in vacuum:
When solving problems, the value c = 3 · 10 8 km/s is usually taken for calculations.
REFLECTION OF LIGHT
A wave surface is a set of points oscillating in the same phase.
Huygens' principle: Each point to which the disturbance has reached itself becomes a source of secondary spherical waves.
Laws of light reflection
MN - reflective surface
AA 1 and BB 1 - rays of incident plane wave
AA 2 and BB 2 - reflected plane wave rays
AC - wave surface incident plane wave is perpendicular to the incident rays
DB - wave surface of the reflected plane wave perpendicular to the reflected rays
α - angle of incidence (between the incident beam and perpendicular to the reflecting surface)
β - reflection angle (between the reflected ray and perpendicular to the reflecting surface)
Laws of reflection:
1. The incident ray, the reflected ray and the perpendicular reconstructed at the point of incidence of the ray lie in the same plane.
2. Angle of incidence equal to angle reflections.
REFRACTION OF LIGHT
Refraction of light is a change in the direction of propagation of light when passing through the interface between two media.
Laws of light refraction:
1. The incident beam and the refracted beam lie in the same plane with a perpendicular to the interface between the two media, restored at the point of incidence of the beam.
2. The ratio of the sine of the angle of incidence to the sine of the angle of refraction for two given media is a constant value 
where n is relative indicator refraction (otherwise the refractive index of the second medium relative to the first)
Refractive index
Physical meaning: it shows how many times the speed of light in the medium from which the beam exits is greater than the speed of light in the medium into which it enters.
FULL INTERNAL LIGHT REFLECTION
Let absolute indicator refractive index of the first medium is greater than the absolute refractive index of the second medium 
, that is, the first medium is optically denser. 
Then, if he sends
