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electric field potential capacitance
The graphics and text organize the logical sequence of Coulomb's law - electric field - electric potential energy - electric potential - capacitance, the basic interaction between stationary charges, and the knowledge of the movement of charged particles in the electric field. Friends can download it and use it.
Edited at 2023-03-31 09:12:31
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electric field potential capacitance
- One Hundred Years of Solitude Character Relationship Chart
One Hundred Years of Solitude is the masterpiece of Gabriel Garcia Marquez. Reading this book begins with making sense of the characters' relationships, which are centered on the Buendía family and tells the story of the family's prosperity and decline, internal relationships and political struggles, self-mixing and rebirth over the course of a hundred years.
- One Hundred Years of Solitude Character Relationship Chart
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Project management is the process of applying specialized knowledge, skills, tools, and methods to project activities so that the project can achieve or exceed the set needs and expectations within the constraints of limited resources. This diagram provides a comprehensive overview of the 8 components of the project management process and can be used as a generic template for direct application.
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Electric field, potential and capacitance
Basic interactions between stationary charges
Coulomb's law
Coulom's_law the magnitude of the electrostatic force of attraction or repulsion between two point charges is directly proportional to the product of the magnitudes of charges and inversely proportional to the square of the distance between them.The force is along the straight line joining the two charges.If the charges have the same sign, the electrostatic force between them is repulsive; if they have different signs, the force between them is attractive. The magnitude of the electrostatic attraction or repulsion between two point charges in a vacuum is proportional to the product of the magnitudes of the charges and inversely proportional to the square of the distance between them. The force is along the line joining the two charges. If the charges have the same sign, the electrostatic force between them is repulsive; if they have different signs, the force between them is attractive First published by French physicist Charles-Augustin de Coulomb in 1785, this is a natural/natural law!
Replacing the negative charge with a different charge or quantity |q| is called a "test charge", and the other constant charge Q is called a "field source charge" or "source charge". No matter how the negative charge is replaced, the position r from the positive charge has an unchanged component, which we call the "Electric field".
electric field
When the source charge Q/distance r from Q do not change, the inside of the box is the unchanged part: ke is called Coulomb's constant (we also call it the electrostatic force constant) This part inside the box is called the "electric field"
The electric field is the Coulomb force/electrostatic force/electric field force exerted by a unit (trial) charge.
The electric field is the force exerted by a unit charge
The gravitational field is g The gravitational field is the force exerted on an object per unit mass. g is also called acceleration. What are the properties of the electric field E?
Electric field and electric field strength are synonymous. The size of the electric field is the intensity of the electric field, and the electric field should be the dominant one. There is no such word in English as electric field strength
The layout rules of electric field
The electric field of a point charge is not equal everywhere. According to Coulomb's law, the formula conversion is as shown on the left Note: Which is the definition? Which is the root cause?
related to the speed of light
virtual electric field lines Marked with dots as charges, "electric field lines" are radiated. It should be noted that field lines are graphical illustrations of the strength and direction of an electric field and do not represent actual physical meaning. But according to actual conditions, the number of these virtual electric field lines is indeed proportional to the amount of charge. Assume that the number of electric field lines is the number of charges! Characteristics of electric field lines: Electric field lines never intersect! Terminates at negative charge or at infinity. What is the relationship between electric field strength E and electric field lines?
Electric field lines are three-dimensional and uniform divergence of source charges, just like light illumination. The surface area of the ball at a distance r is 4πr^2,
How many electric field lines are there in 1 unit of surface area "A"? r is a variable, there is no need to study the electric field lines at 2r and 3r Inverse-square law, meaning: geometric dilution of point source radiation in three-dimensional space - diffusion
The electric field E is 1/ε times the density of the electric field lines and 1/ε times the density of the charge --- this is the root cause!
1. Where the distance from the source charge is equal, the magnitude of the electric field is the same; 2. The denser the electric field lines, the greater the electric field; the sparser the electric field lines, the smaller the electric field; The density of the electric field lines is the intensity of the electric field.
Multiple electric fields at a certain point can be vectorially synthesized/each calculates its own spherical radius The curved electric field lines are the sum of all electric fields.
Static shielding
1. Conductor electrostatic balance 2. Faraday Cage. The induced charge creates an opposing electric field that cancels out the electric field outside the cage.
Conditions for the validity of Coulomb's law
1. The charge is spherically symmetrically distributed (for example: point charge or charged metal ball), because the Coulomb constant k is related to the spherical shape. In the picture on the right, there are conductors around the charge, which affects the uniform distribution of the electric field intensity. The Coulomb force at a certain point is not suitable for Coulomb's law; However, knowing the electric field strength at a certain point, can we calculate the Coulomb force? sure.
2. Charges must be stationary relative to each other.
Logical summary of electric field
Basic interaction between stationary charges → force
The electric field is the force exerted by a unit charge
The density of electric field lines can represent the density of charge
The density of the electric field lines represents the intensity of the electric field.
potential
electrical potential energy
basic logic
The electric field is the force exerted by a unit charge, and any charge in the electric field Q will be affected by the force. Energy and force are directly related. If a force is applied, energy must exist there.
Electric potential energy of point charge electric field
Electric potential energy of positive charge electric field
1. Work done by Coulomb force
Work done by Coulomb force Test the charge q under the action of Coulomb force. From point B to point A, Coulomb force does positive work. According to the law of conservation of energy, the positive work done is the reduced electrical potential energy. The negative sign refers to the reduced electrical potential energy, which is the same as the work done. Energy has only magnitude and no direction.
The electrical potential energy at point B is greater than the electrical potential energy at point A
The amount of work done by the Coulomb force is the difference in electric potential energy. The level of electric potential energy can be judged by the work done.
2. Coulomb force is a variable force, and the amount of work done by the variable force
Coulomb force is a variable force Test the point charge q, and the Coulomb force does work from point B to point A. The Coulomb force is a variable force related to the position. If the displacement changes a little, the force will change.
Mathematical graph (integral) of work done by Coulomb force as a variable force, it is recommended to remember the conclusion
3. Coulomb force changes from A→∞
When Coulomb force changes from A→∞, F→0 Test charge q under the action of Coulomb force, from point A to infinity, Coulomb force does positive work, the formula of the law of conservation of energy: The negative sign means that reduced work is increased electrical potential energy and vice versa. Energy has only magnitude and no direction.
The total work done by the Coulomb force is the electric potential energy at that point
1. The zero point of electric potential energy is at infinity, and the Coulomb force is zero at infinity. The amount of work done from point A to zero is the electric potential energy at that point; 2. The magnitude of the electric potential energy surrounding a charge is directly proportional to the quantity of the test charge and inversely proportional to the distance from the source charge.
Electric potential energy of negative charge electric field
The work done by the Coulomb force is the difference in electrical potential energy between two points
Test charge q is under the action of Coulomb force. From point A to point B, Coulomb force does positive work. According to the law of conservation of energy, the reduced electric potential energy is the work done by Coulomb force.
The electrical potential energy at point A is greater than the electrical potential energy at point B
The amount of work done between two points
Test the point charge q and the amount of work done by the electric field force from point A to point B:
From this point, all the work done by the external force to overcome the Coulomb force (uniform speed and extremely slow speed) is the electric potential energy at that point.
The increased electrical potential energy is the work done to overcome the Coulomb force
The electric potential energy around negative charges is negative, and the electric potential energy at infinity is 0; The closer to the negative charge, the greater the absolute value of the electrical potential energy.
Point charge potential energy change
Electric field force and work-----Electric field force and electric potential energy------Work and potential energy difference
The changing rules of electric potential energy of point charge
1. Force is the gradient of work and potential energy gradient (negative value); refer to the potential energy diagram of single charge, positive and negative charges 2. The position where |electric potential energy| is larger, the greater the force; 3. Where the force is greater, the electric field is greater.
Electric potential energy of uniform electric field
uniform electric field
The purple box can be seen as a uniform electric field
Test the charge q under the action of Coulomb force, and the Coulomb force does positive work from point A to point B. According to the law of conservation of energy, the work done is the reduction of electrical potential energy, and the negative sign represents the reduction of electrical potential energy.
The electrical potential energy at point A is greater than the electrical potential energy at point B
Coulomb force is a constant force, the work done from A→B
The maximum electric potential energy of a uniform electric field, d: plate spacing Where is the zero point of electric potential energy?
Uniform electric field potential energy change
Uniform strength: the size of the electric field is the same everywhere, and the electric field force is the same everywhere; pay attention to the zero point of the electric potential energy
What is the electrical potential energy at point M?
Why is the distance in the electric potential energy formula of a uniform electric field opposite to the distance in the point charge potential energy formula?
Because E changes for a point charge, the potential energy is inversely proportional to the distance from the source charge.
The uniform electric field E is determined by
It is meaningless to compare electric potential energies in different systems
Useful Byproducts of Coulomb's Law
The electric field strength is 1/ε of the charge density ---This formula is not limited to point charge electric field →1/ε of the charge amount per unit area is the electric field strength
Electric field strength composed of parallel plate conductors Q: Number of positive or negative charges on the plate S: area of the board ε: Dielectric constant, ε0 vacuum dielectric constant
unit of electrical potential energy
Electric potential energy is defined according to the work done by the electric field force, so the unit of electric potential energy is the same as the unit of work, Joule, symbol J
Logical summary of electric potential energy
If an object is acted upon by a force, energy must be present there. Force is a gradient of energy.
Electric field is force field The positive work done by the electric field force is the reduced electric potential energy
Determine the position where there is no electric field force (or the force is balanced) as the 0 reference point The net force is zero, the electric field is 0, and the electric potential energy is zero
All the positive work done by the electric field force starting from a certain point represents the electric potential energy at that point.
Definition of electric potential
The pursuit of unified laws is the driving force for the development of physics. Unified laws require eliminating variables as much as possible! The electric potential is the electric potential energy without the influence of the test charge. The electric potential is the electric potential energy possessed by the unit charge in the electric field. SI unit Volt (Volt), symbol V, or J/C
A charge with a charge quantity of 1 C at this point The electric potential energy is 1 J, then the electric potential at this point is 1 V.
electric potential of point charge electric field
r: distance from source charge
Yellow is 0V. The darker the color (→purple or →blue), the greater the absolute value of the potential. 1. The electric potential gradually decreases along the direction of the electric field line until the zero point of the electric potential energy. 2. After passing the zero point of electric potential energy, the electric potential calculated as a negative value also gradually decreases (according to an absolute value, it increases) 3. The electric potential completely corresponds to the zero point position of the electric potential energy. It has only magnitude but no direction. It is a scalar quantity. 4. Thin lines and circles represent equal electric potentials, and also represent equal electric potential energy (/C)
Electric potential of a uniform electric field
l: distance from the negatively charged plate
Potential difference
potential difference of point charge
Blue: potential difference
potential difference of uniform electric field
The potential difference between two points AB, also called voltage, is the work done by unit charge and the difference in electric potential energy of unit charge. is the work done by unit charge Ed, d: the distance between points AB The electric field between AB is equal/the linear density is equal
Board spacing
All potential energy of charge q is converted into kinetic energy
Logical summary of electric potential
Electric potential is the electrical potential energy possessed by a unit charge in an electric field
It is usually specified that the electric potential energy at infinite distance is 0, or that the electric potential energy at the surface of the earth is 0. The zero point of electric potential is the same as the zero point of electric potential energy
The potential difference between any two points is the work done by a unit charge moving between the two points.
Electric field-electric potential energy-electric potential summary
point charge
1. Thick black lines with arrows: electric field lines - electric field force lines; the density of the line at a certain point is the size of the electric field, the size of the electric field force, and the density of the charge; The field lines do not cross. Along the direction of the electric field lines, the smaller the density of the lines, the smaller the electric field and the smaller the electric field force; 2. Color and depth represent electric potential energy: yellow represents zero electric potential energy. The darker the color, the greater the |electric potential energy|; the electric potential at 0 electric potential energy is 0; 3. The thin coil represents the equipotential surface; it is also the surface with equal electric potential energy. 4. The denser the electric field lines, the greater the electric field force, the more work done at the same distance, the greater the electric potential energy, and the denser the equipotential lines. 5. The electric field lines are perpendicular to the equipotential surface, and the electric potential gradually decreases along the direction of the electric field lines;
uniform electric field
A stable and uniform electric field can be constructed through the amount of charge
capacitance
There is an interaction between stationary charges
electric field force
electric field
electrical potential energy
Electric potential and potential difference
Connect two conductive plates to the power supply. After the positive and negative charges on the plates are balanced, then turn off the power. The two plates will store energy.
What is a capacitor?
The electric field of two parallel plates, the positive/negative charges are balanced, and the component that can store charges is called a capacitor. Typically consists of two conductive surface plates separated by an insulating layer called a dielectric in between. In a conventional capacitor, electrical energy is stored statically by separated charges (usually electrons) in an electric field between two electrode plates. <This component can store energy and is a container for storing charge, so it is called a capacitor>
Definition of capacitor
Q: The amount of charge carried by a capacitor refers to the amount of charge carried by one plate. U: potential difference between the two plates of the capacitor Capacitance: the amount of charge stored per unit voltage
In the SI International System of Units, the unit of capacitance is farad (farad), abbreviated as method, symbol: F. That is, when the capacitor carries a charge of 1 C, the potential difference between the two plates is 1 V, and the capacitance of the capacitor is 1 F. The F unit is very large, and the units commonly used in practice are mainly microfarads (μF) and picofarads (pF). 1 μF = 10^-6F 1 pF = 10^-12F
From the formula, it seems that the size of the capacitor is affected by the amount of charge and voltage, but it is not! Voltage itself is the amount of charge
Ideally, the capacitance size depends on the plate area and the thickness of the dielectric. The capacitance size is fixed when each specific capacitor is manufactured. (Except variable capacitors)
Dielectric
Common dielectrics (dielectric materials) are: Ceramics, films (plastics, paper), mica, glass, paper, air, vacuum Oxide layers on metals (aluminum, tantalum, niobium),
1. Left picture: If any conductor is added in the middle of the plate, the charge will flow and energy will be lost. So a dielectric is an insulator. 2. Dielectrics can be polarized by an applied electric field. Material polarization is similar to electrostatic induction (middle image). 3. Dielectric materials have no loosely bound or free electrons. When placed in an electric field, the charges in the dielectric do not flow out of the material, but only slightly deviate from their original average equilibrium position. (picture on the right)
Ceramic capacitors
Cross-sectional structure and schematic diagram of chip capacitor. Do I need to distinguish between positive and negative poles when using it?
Film capacitor
Polypropylene (PP) Polyethylene terephthalate, polyester (PET) Polyphenylene sulfide (PPS) Polyethylene naphthalate (PEN) Polytetrafluoroethylene (PTFE) Do I need to distinguish between positive and negative poles when using it?
electrolytic capacitor
Aluminum electrolytic capacitors 1. The anode is aluminum foil, and there is an oxide layer of aluminum oxide attached to the aluminum foil. The oxide layer is a dielectric! 2. The paper soaked in electrolyte is the cathode, and the aluminum foil in the paper is just the cathode lead; 3. Electrolytic capacitors are named after the cathode material is an electrolyte. 4. It is necessary to distinguish between positive and negative poles. Ceramics and film capacitors all refer to dielectrics. This picture shows metal oxide layer dielectrics.
Tantalum capacitor
Distinguish between positive and negative poles Positive electrode: tantalum block Negative electrode: manganese dioxide The dielectric is tantalum pentoxide
Different dielectrics have a huge impact on capacitance
Permittivity
Super capacitor
1. Super: The energy density of the capacitor is large, that is, the energy that can be stored per unit volume. Comparing the upper and lower figures, the capacitance value of supercapacitors is up to 20,000 times that of electrolytic capacitors. 2. The energy density of existing supercapacitors is about 10% of traditional batteries/rechargeable batteries. The energy density of traditional capacitors is extremely low, and there is a huge gap between it and rechargeable batteries. Supercapacitors are in the middle of the gap and have an obvious role in making up for it. Can achieve up to 12,000 Farads/1.2 Volts. 3. While the energy density of existing supercapacitors is about 10% of that of traditional batteries, their power density is typically 10 to 100 times higher. Power density is the product of energy density times the speed at which energy is delivered to the load (in energy converters such as batteries, motors, power supplies, etc., power density is expressed in W/m^3). High power density results in short charge/discharge cycles. This makes them ideal for paralleling with batteries and can improve battery performance in terms of power density.
A supercapacitor (electrochemical capacitor) consists of two electrodes separated by an ion-permeable membrane (separator) and an electrolyte that ionically connects the two electrodes. When an electrode is polarized by an applied voltage, the ions in the electrolyte form an electric double layer of opposite polarity to the electrode.
Rated voltage
Rated voltage
Above a certain electric field strength, the dielectric in the capacitor becomes conductive and loses its capacitive function. Thin The rated voltage marked on the product must be lower than the breakdown voltage.
Charged particles move in an electric field
Should be positioned as basic learning
1. The heating wire heats the cathode and releases electrons; the electron beam is controlled to form and focus; 2. The electrons are attracted by the considerable positive electrode potential (usually focusing the positive electrode 1200V, accelerating the positive electrode 2000V) to form a very thin electron beam with a certain speed; 3. Apply external electric fields on the y (vertical) and x (horizontal) plates to deflect the electron beam; 4. The electric beam hits a display screen coated with photosensitive material, a fluorescent screen with small dots of phosphorescent material, which is detected as light.
Principle of deflection system
The force deflection of charges in an electric field! The electrons are accelerated by a positive voltage at the anode and pass through the hole in the anode. A vertical Y deflection is archived by a plate capacitor. The signal to be measured is sent to the vertical plate capacitor. Depending on the voltage, the electrons are deflected up or down, they follow the measured voltage signal. In the X-direction, the deflection takes place by a 90° angle turned plate capacitor, to which a sawtooth voltage is applied. This ensures that the beam is always deflected from left to right. The electrons are accelerated by the positive voltage on the anode and pass through the hole in the anode. Vertical Y deflection is achieved by plate capacitors. The signal to be measured is sent to the vertical plate capacitor. Depending on the voltage, the electrons are deflected upward or downward, and they follow the measured voltage signal. In the X direction, the deflection of the electrons is caused by another plate capacitor at a 90° angle. Applying a sawtooth voltage to it ensures that the electron beam is always deflected from left to right.
The external voltage signal to be measured forms a y (vertical) electric field that causes the electrons to move up and down. The electrons are constantly stacked on the display screen, but only one vertical line can be seen. (Similar to the up and down movement of a spring vibrator).
The sawtooth voltage applied by a single x (horizontal) capacitor deflects the electrons all the way to the right, unfolding the signal under test in time to form a waveform to find the problem. The frequency of the sawtooth voltage signal should be synchronized with the frequency of the measured signal
The deflection plate is the capacitance; the Y-axis is the amplitude and motion displacement, and the X-axis is time! The signal to be measured is mainly the voltage value, and all quantities that can be measured with a voltmeter can be input on the Y-axis. The value and period of AC voltage can also be measured.