potential

[diàn shì]

physical quantity

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zero

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electrostatic field The scalar potential of is called electric potential, or Electrostatic potential 。 stay electric field Middle, some Point charge Of Electric potential energy It is the ratio of the amount of charge it carries (related to the positive and negative. When calculating, the electric potential energy and the positive and negative of the charge are brought in to judge the size of the electric potential at this point, as well as the positive and negative). It is called the potential at this point (also called the potential), and is usually expressed in φ. The potential is derived from energy Angular physical quantity ， electric field intensity The electric field is described from the perspective of force. Potential difference energy Closed circuit Generated in electric current (When the potential difference is quite large, air, etc insulator Will also become conductor ）。 Potential is also called potential.

Chinese name: potential
Foreign name: electric potential
Alias: potential

expression: φA=Ep/q
Applicable fields: Electronics, physics
Applied discipline: physics

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Potential gradient: electric dipole distribution diagram

stay Electrostatics Li, potential (electric potential) (also called potential) is defined as: electric field At a location in Unit charge Owned Electric potential energy The ratio to the amount of electric charge it carries. The potential has only size, no direction - yes scalar , its value has no absolute meaning, only relative meaning.

(1) Unit positive charge The ratio of the work done by the electric field force to the amount charged when it is moved from a point A in the electric field to the reference point O (i.e. zero potential energy point, generally taken as infinite or zero potential energy point on the earth).

So φ A=Ep/q. stay International System of Units The units in are Volts ( V )。

(2) The difference between the potential of a point in the electric field and the reference point O is called the potential of the point.

"The electric potential of a point in the electric field is numerically equal to the electric potential energy of the unit positive charge at that point".

Formula: ε=q φ (where ε is electric potential energy, q is charge quantity, φ is electric potential), that is, φ=ε/q

In an electric field, the electric potential energy of a point's charge is the same as that of its Charge quantity The ratio is one constant , which is independent of the charge itself physical quantity It has nothing to do with the existence of electric charges, and is a physical quantity determined by the nature of the electric field itself.

Electric potential is a kind of electrostatic field Scalar field 。 The basic property of the electrostatic field is that it has a force on the charge placed in it, so when moving the charge in the electrostatic field, the electrostatic field force must do work. However, when the charge moves along any path in the electrostatic field and returns to its original position once a week, the work done by the electric field force is always zero, that is, the work done by the electrostatic field force is independent of the path, or the loop integral of the electrostatic field strength is always zero.^[1]

This property of electrostatic field is called electrostatic field loop theorem 。 According to this property, electric potential can be introduced to describe electric field, as if field of gravity The work done by the medium gravity is independent of the path, and the gravity field can be described by the gravity potential. The potential of a point in the electric field is defined as the work done by the electric field force when the unit positive charge moves from the point to the point where the potential is zero. Generally, the potential of an infinite point is zero, so the potential of a certain point is equal to the work done by the electric field force when the unit positive charge is moved from the point to infinity, which is expressed as:

The unit of potential is V (V), 1V=1J/C (1J/library). The points with equal electric potential in the electrostatic field form some surfaces, which are called Equipotential surface 。 power line Always with equipotential surface orthogonal And points to the direction of potential reduction, so the distribution of electric field on the equipotential surface in the electrostatic field is drawn. Although the electric potential is an auxiliary quantity introduced to describe the electric field, it is a scalar quantity vector The calculation is simple. In many specific problems, the electric potential is calculated first, and then the field strength is calculated through the relationship between the electric potential and the field strength. Potential and potential difference (voltage) are very useful concepts in circuit problems. Electric potential is a general description of electric field Electromagnetic potential A special case of.^[1]

Physical principles

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Potential gradient

(1) The charge of charged quantity q moves from a point A in the electric field to the reference point O (i.e. zero potential energy point, which is generally taken as the zero potential energy point at infinity or the earth), Electric field force Work W AO (The work done by the electric field force to move this charge from point A to zero potential energy point) and the electric quantity q ratio of this charge is called (AO two-point potential difference) point A potential

The potential has only magnitude, no direction, and is scalar. Like topography, potential is also of relative significance. In specific applications, the potential energy at the standard position is often taken as zero, so the potential at the standard position is also zero. The potential is simply the result of comparing it with the standard position. We often take the earth as the standard position; In theoretical research, we often take the infinite distance as the standard position. In practice, we often use the expression "outside the electric field" to replace the "zero potential position". Electric potential is a relative quantity, and its reference point can be arbitrarily selected. No matter whether the selected object is charged or not, it can be selected as the standard position - zero reference point. For example, the earth itself is negatively charged, and its potential is about 8.2 × 10 ^ 8V relative to infinity. However, the earth can still be regarded as the zero potential reference point. At the same time, since the earth itself is a large conductor with a large capacitance, adding or removing some charges on such a large conductor has little effect on its potential change. Its potential is relatively stable. Therefore, in general, the earth is chosen as the zero potential reference point.

The characteristics of electric potential are: no matter the electric field line of positive charge or negative charge, the direction along the electric field line is always the direction of potential reduction, and the direction against the electric field line is always the direction of potential increase.

The potential of each point in the positive charge electric field is positive, far away from the positive charge, and the potential decreases.

The potential of each point in the negative charge electric field is negative, far away from the negative charge, and the potential increases.

Physical meaning:

(1) Determined by the position of a point in the electric field, reflecting Electric field energy The nature of.

(2) It has nothing to do with the inspection of charge quantity and electrical property.

(3) It represents the work done by the electric field force to move the 1C positive charge to the reference point.

Relationship between potential difference and potential:

∵

∴

Work done by electric field force:

① Formula: W=qU

②

▄ U is determined by the position of two points in the electric field

 W is determined by q and U. W has nothing to do with the path. Like gravity, it belongs to Conservatism Do work.

③ Features: The work done by the electric field force is determined by the moving charge and the electric potential difference, independent of the path.

The formula and derivation of the potential difference and potential of the electrostatic field generated around the charge: for a positive charge whose charge is Q, there is an outward radiation electric field around it. Take any electric field line, take any point A on it as r from the electric charge of the field source, and place a point charge of q at point A. Make it move a small displacement △ x along the electric field line under the action of the electric field force. Since this displacement is very small, it is considered that the electric field force has not changed on this displacement, so φ=KQ (1/r) is obtained.^[2]

Physical methods

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Potential gradient

(1) It is determined by the position of a point in the electric field, reflecting the nature of the electric field energy.

(2) It has nothing to do with the inspection of charge quantity and electrical property.

(3) It represents the work done by the electric field force to move the 1C positive charge from the reference point to the zero potential point.

Generated around an electric charge electrostatic field Formula and derivation of potential difference and potential of

The point charge of a field source is Q, and there is a point charge of q at point A with a distance of r from Q. It is verified that the potential at point A is

Prove that we take r (i+1) - r (i)=△ r, △ r → 0

Then r (i+1) to r (i), that is, △ r Coulomb force It can be seen as constant F(r(i))=kQq/(r(i))^2

Then the work done by the Coulomb force in this section:

△W(i)≈F(r(i))·△r=kQq·△r/(r(i))^2≈kQq·△r/(r(i)·r(i+1))=

KQq · (r (i+1) - r (i))/(r (i) · r (i+1))=kQq · (1/r (i) - 1/r (i+1))

∑△ W (i)=W=kQq/r (1) - kQq/r (n) to get the formula

Potential distribution of the same amount of point charge:

(1) On the positive charge line: the midpoint potential is the lowest, and the potential gradually increases from the midpoint to both sides;

(2) On the middle vertical line of the line: the potential decreases from the midpoint to both sides of the middle vertical line until the potential is zero at infinity;

(3) The negative point charge is just the opposite.

Equal heterogeneous point charge potential distribution:

(1) On the line of point charge: along the direction of electric field line, the electric potential decreases from positive charge to negative charge;

(2) On the central vertical line of the line: the potential difference between any two points on the central vertical line is zero, that is, the potential on the central vertical line is zero.

research field

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Cell membrane potential:

Cells It is the basic unit of life activities. Each cell of an organism is surrounded by a cell membrane with a thickness of about (60~100) × 10-10 m. The cell membrane is filled with liquid inside and outside, and a certain amount of electrolyte 。 The cell membrane is composed of two lecithin layers with molecular thickness called lipid bilayer. Lecithin molecule is an amphiphilic molecule. Its hydrophobic chain goes to the middle of the membrane, and its hydrophilic part extends to the inner and outer sides of the membrane. Spherical protein molecules are distributed in the membrane. Some protein molecules are partially embedded in the membrane, some are outside the membrane, and some protein molecules span the entire membrane. These membrane proteins play a catalytic role in biological activity transfer and many chemical reactions, and act as channels for ions to pass through the membrane. Cell membrane plays a key role in cell metabolism and information transmission of organisms.

In the electrolyte inside and outside the cell membrane, K + Ion ratio Na + And Cl - Ions are easier to penetrate the cell membrane, so K on both sides of the cell membrane + The concentration difference of ions is the largest. K in resting nerve cell fluid + The concentration of ions is about 35 times that of extracellular ions. For simplicity, Na is not considered + 、Cl - And H two O penetration of cell membrane, only K + Ions penetrate the cell membrane. Membrane potential is the potential difference caused by the concentration difference between the two sides of the membrane due to the selective penetration of ions on both sides of the membrane. It refers to the balance potential difference between the two sides of the membrane. Appropriate devices shall be provided to form the following batteries from intracellular and extracellular liquids:

Because of K in intracellular liquid phase + Ion concentration ratio. The concentration in the phase is high, so K + Ions tend to diffuse from beta phase through the membrane to the extracellular liquid alpha phase, resulting in a net positive charge on one side of alpha phase and a negative charge on the other side of beta phase. The positive charge generated on the alpha side will prevent K + Further diffusion to α phase, and the negative charge generated by β phase will accelerate K + It diffuses from α phase to β phase, and finally reaches dynamic equilibrium. At this time, K + The electrochemical potential of ions in α and β phases is equal, because K + The ions transfer from β phase to α phase, resulting in the potential of α phase higher than that of β phase.

In biochemistry, it is customary to use the following formula: membrane potential.

The existence of cell membrane potential means that there is a double electric layer on the cell membrane, which is equivalent to the distribution of some dipole molecules cell surface 。 For example, when the heart muscle contracts and relaxes, the potential of the myocardial cell membrane changes constantly, so the total dipole moment of the heart and the electric field generated by the heart are also changing. Electrocardiogram (ECG) is to measure the change of potential difference with time caused by the change of cardiac dipole moment between several groups of symmetrical points on the human body surface, so as to judge whether the heart works normally. Similar electromyogram is used to monitor the electrical activity of muscles, which is helpful to guide athletes in training. EEG is to monitor the change of potential difference between two points on the scalp over time to understand the electrical activity of brain nerve cells. Experiments show that our thinking and receiving external feelings through visual, auditory and tactile organs are all related to changes in cell membrane potential. Understanding life requires understanding how these potential differences are maintained and how they change. This research field is attracting more and more attention.

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Superconducting junction and coupling superconducting junction:

(1) thermal noise Multiple increase and multiple decrease of electrostatic potential in superconducting junction: researchers have studied the electrostatic potential at both ends of superconducting junction under the conditions of over damping and under damping, taking into account thermal noise and the simultaneous input of AC and DC signals. The research shows that with the increase of temperature (the intensity of thermal noise is proportional to the temperature), the electrostatic potential will be increased and decreased for many times (the peak value of electrostatic potential increased for many times corresponds to the resonance activation of electrostatic potential). In addition, the electrostatic potential at both ends of the superconducting junction also shows that the thermal noise (caused by noise) is strengthened and stabilized.

(2) The emergence of spatiotemporal noise in coupled superconducting junction systems (or devices) and its impact on transport: in this study, researchers first found that spatiotemporal noise may appear in coupled superconducting junction systems (a Superconducting quantum interference device ）And the correlation between the spatiotemporal noise and the difference of the wave function of the electron pair Symmetry breaking Can cause transport. By studying two models (a Gaussian noise model and a telegraph noise model), researchers found that the probability flow in the studied coupled superconducting junction system is always negative and a "well" will appear with the increase of thermal noise intensity. According to the research results of the researchers, the researchers can control the noise to make the probability flow in a state favorable to the experimental requirements of the researchers. For example, if researchers want to get a large negative probability flow in the experiment, they can take the following two measures: a) Under certain environmental disturbance, we can properly adjust the temperature to make the negative probability flow near the "well" mentioned above (the intensity of thermal noise is proportional to the temperature), so as to obtain the results favorable to our experimental requirements; b) At a certain temperature, researchers should take certain measures to adjust the environmental disturbance to make the absolute value of negative probability flow as large as possible.

(3) Chaotic noise transport in a thermal inertial "ratchet" superconducting quantum interference device (coupled superconducting junction): Chaotic noise transport in a thermal inertial "ratchet" superconducting quantum interference device with periodic signal input is studied. The research shows that by controlling the temperature and the intensity of the external input signal, researchers can make the direction of the transport sign inversely. When the temperature is low enough, researchers can easily get chaotic transport; However, when the temperature is high enough, the transport is mainly thermal noise transport.

(4) Coupled superconductor junction under environmental disturbance: researchers studied a SQUID [superconducting quantum interference device (coupled superconductor junction)] considering the internal thermal fluctuation and external environmental disturbance, and found that the external environmental disturbance can cause transport in SQUID, and the electrostatic potential can be reversed by controlling the correlation between the internal thermal fluctuation and the external environmental disturbance; It is found that the current voltage characteristic is more and more close to Ohm's law under normal conditions with the increase of the internal temperature of the system.

(5) The correlation between thermal fluctuations and environmental disturbances can cause electrostatic potential in a single superconducting junction: they have aroused a large number of researchers' interest internationally. In related papers, researchers have studied the electrostatic potential in superconducting junctions caused by the correlation between noise caused by external environmental disturbances and internal thermal fluctuations. It is shown that the correlation between the thermal fluctuations in the system and the disturbances in the external environment can cause symmetry breaking, which can lead to electrostatic potential in the superconducting junction.^[3]

Famous scholars

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Volts (Alessandro Vlota, 1745-1827), Italian physicist. Born in Como on February 18, 1745, he studied natural phenomena out of curiosity when he was an adult. In 1774, Volt became a preparatory professor of physics at Como University.

Volts He has made many important contributions to physics. He has invented the starter, electroscope, storage device and other electrostatic experimental instruments^[4] 。

Volts The most remarkable achievement is the invention of Volts Battery. Volts The emergence of batteries has a profound impact on the development of electricity, creating a new vast world and becoming the most powerful weapon for human beings to conquer nature. Volt became the first great inventor to make human beings obtain continuous current^[4] 。

In 1786 and 1792, Gavani observed in his experiments that the legs of frogs hung with copper hooks would spasm when they hit the iron frame. He believes this is the effect of bioelectricity. Volts It is believed that the above phenomenon is due to the electric effect produced when two different metals contact. The two viewpoints have caused controversy for ten years. During this period, Volts A large number of experiments have been carried out. He successively used a variety of different metals, put them in various liquids for hundreds of experiments, and finally invented Volts Battery. In 1800, he officially Royal Society Reported his discovery, from then on, the device that generates steady current has played a huge role in electromagnetic research^[4] 。

The unit of potential, potential difference and electromotive force of driving current in the International System of Units, volt, is named after him in memory of him.^[5]

Proper noun

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Electric potential energy

electrostatic field In potential energy 。 one Point charge When the difference between the electric potential energy of a certain two points (such as point A and point B) in the electrostatic field is equal to its movement from point A to point B, Electrostatic force Work done. So WAB=qEd (E is the electric field intensity , d is along Electric field line The electric potential energy is shared by electric charge and electric field, and has unity.

The electric potential energy reflects the common energy 。

The electric potential energy can be determined by Electric field force Work Because W AB =qU AB =q（ΦA- ΦB)=qΦA-qΦB=E pA (Initial) - E pB (end)=- △ E p ，

(where Φ is the potential and q is the potential Charge quantity , U is Potential difference ，E A 、E B Is the electric potential energy of two points. Note that Ep is the initial state minus the final state).

Relation between work done by electric field force and electric potential energy change:

WAB>0, △ Ep<0, electric field force Positive work , electric potential energy is reduced and converted into other forms of energy;

WAB<0, △ Ep>0, electric field force Negative work , electric potential energy increases~other forms of energy are converted into electric potential energy.

along Electric field line , A → B movement, if it is positive charge , then WAB>0, then UAB=Φ A - Φ B>0, then Φ ↓, then positive Ep ↓;

if it is negative charge , then WAB<0, then UAB=Φ A - Φ B>0, then Φ ↓, then negative Ep ↑.

Move against the electric field line, B → A, if it is positive charge , WBA<0, UBA=Φ B - Φ A<0, Φ ↑, positive Ep ↑;

If it is negative charge, WBA>0, UBA=Φ B - Φ A<0, Φ ↑, negative Ep ↓;

The work done by electrostatic force is equal to the reduction of electric potential energy.

Wab=Epa-Epb

The electric potential energy formula is related to the electric field, the charge in the electric field and the selection of the zero point of the electric potential energy（ Electricity Is the electrostatic field generated by q), where the electric potential energy and charge q are located spatial location The distance r to the point charge location has the following relationship: We=kQq/r. Where k is constant 。

Don't notice here minus sign , and gravitation The potential is different, because the gravitational direction is pointing to each other. When Q and q are both positive signs, the electric field force（ Coulomb force ）They are mutually exclusive.

charge The electric potential energy of a point in the electric field is equal to the work done by the electric force when the electric charge is moved from the point to the point where the electric potential energy is zero.

Size judgment

1. Judgment method of field source charge: the closer to the positive charge of the field source, the greater the electric potential energy of the positive charge, and the smaller the electric potential energy of the negative charge

2. Electric field line method: when the positive charge moves along the direction of the electric field line, the electric potential energy gradually decreases, and when it moves against the direction of the electric field line, the electric potential energy gradually increases

When the negative charge moves along the direction of the electric field line, the electric potential energy gradually increases, and when it moves against the direction of the electric field line, the electric potential energy gradually decreases

3. Judgment method of work: no matter the positive and negative charges, the electric potential energy of the charge must be reduced when the electric force does positive work, and the electric potential energy of the charge must be increased when the electric force does negative work

The zero potential energy can be chosen arbitrarily, but in theoretical research, the electric potential energy of the infinite distance or the earth is often taken as 0

Take infinity as potential zero: ① Φ>0 in the electric field generated by positive charge, away from Field source charge Φ ↓: moving positive test charge W>0, Ep ↓;

Moving negative test charge W<0, Ep ↑.

② . Φ<0 in the electric field generated by negative charge, keep away from Field source charge Φ ↑: moving positive test charge W<0, Ep ↑;

Moving negative inspection charge W>0, Ep ↓.

Attachment:

1. Only under the action of electric field force:

（1） Electric field force When doing positive work, the electric potential energy decreases, kinetic energy Increase. Namely: electric energy is converted into other forms of energy (kinetic energy)

(2) When the electric field force does negative work, the electric potential energy increases and the kinetic energy decreases. That is, other forms of energy (kinetic energy) are converted into electric energy

2. Not only under the action of electric field force:

(1) Electric field force Positive work The electric potential energy is reduced, and the change of kinetic energy is uncertain.

(2) Electric field force Negative work It is uncertain how the kinetic energy changes when the electric potential energy increases.

Note: electric potential energy is scalar 。

Potential difference

a. Establishment of the concept of potential difference:

In the gravity field, the more work an object does under gravity, the greater the height difference between two points.

In the electric field, the more work the charge does under the force of the electric field, the greater the "potential difference" between the two points. Thus, the analogy between the height difference in the gravity field and the electric potential difference in the electric field is established.

Considering that there are: hAB=WAB/mg in the gravity field, hAB represents the height difference between two points in the gravity field, and WAB represents the work done by the gravity of the object moving from A to B.

Then hAB is analogous to the potential difference UAB in the electric field, the work done by gravity is analogous to the work done by the electric force WAB, and the gravity of the object in the gravitational field is analogous to the charge charge q in the electric field, so the expression of the potential difference is obtained:

The potential difference is scalar, U, V, 1V=1J/C

b. Calculation of potential difference:

(1) In addition to the electric field, the electric potential energy is also related to the electric charge, which is similar to the gravitational potential energy.

(2) The potential difference is independent of the charge put in, but only depends on the nature of the electric field itself. For a certain electric field, the potential difference between two points is constant.

(3) The calculation of potential difference is scalar operation, and the positive and negative signs shall be substituted in the calculation. In the calculation, the footmarks of W and U shall correspond, namely:

。

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