What is Electric Potential Energy?

In electrostatics, Electric potential energy is the potential energy of a charge distribution in an electric field, which is related to the configuration of the charge distribution inside the system. The unit of potential energy is Joules. The potential energy is different from the potential. Potential is defined as the potential energy per charge that a charge in an electric field has. The unit of electric potential is volts. ^[1]

Point charge potential energy

In a point charge electric field, the potential energy of a point charge:

Where q and Q are the charge amounts of the migration point charge and the electric field center point charge, the unit is

1. Field source charge judgment method: The closer to the positive charge of the field source, the greater the potential energy of the positive charge, and the smaller the potential energy of the negative charge.

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

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

3. Work judgment method: Regardless of the positive and negative charges, the electric field force does positive work, and the potential energy of the charge must decrease.

The zero potential energy can be arbitrarily selected, but in theoretical research, the potential energy at infinity or earth is often taken to be 0.

Take infinity as potential zero: in the electric field generated by positive charge > 0, keep away

The potential energy stored in a point charge system.

The interaction of electrons with electrons outside the nucleus. ^[4]

Potential energy interaction

In the process of a high-speed electron moving in the direction of an atom, if the distance r is very small, the "self energy" of the atom will affect the electron. The interior of the atom is electrically balanced, and the protons of the atom and the electrons outside the nucleus have a charge amount, so they will act on high-speed electrons through an electric field.

At this time, the amount of change in the potential energy of the electron cannot be completely calculated by the above formula. Because in the case of interaction, the electrons also act on the electrons outside the core through the electric field. The interaction between the two is shown in the figure:

The speed of high-speed electrons will be reduced by the force of the electric field outside the atomic nucleus. At this time, a high-frequency radiation, called "continuous X-ray", is emitted, and this radiation is called "bremsstrahlung".

Electric potential energy interaction 2

If the electrons decelerate under the force of the electric field outside the atomic nucleus and still have sufficient kinetic energy, they will knock the electrons outside the atomic nucleus out of orbit. as the picture shows:

Under the interaction of electric field forces, both electrons and electrons outside the nucleus will deviate from orbits, leaving a "vacancy". At this time, the outer electrons of the atom will transition to this position in the inner layer and emit high-frequency rays with the same energy as the energy level spacing, which is called "identifying X-rays" or "characteristic X-rays".

Elements with an atomic number greater than (including) lithium Li atoms have 2 or more energy levels and can undergo transitions. The energy emitted by a transition is related to the atomic number, which reflects the essential characteristics of the atom. The atom can be identified by measuring the emitted energy.

Potential energy interaction three

Interaction of high-speed electrons with electrons outside the nucleus.

Now carefully analyze the specific process of high-speed electrons interacting with electrons outside the nucleus. as the picture shows:

High-speed electrons move toward the nucleus at speed v1, and electrons outside the nucleus rotate at high speed around the nucleus at linear velocity v2. The nucleus has a centripetal force F2 on the electrons outside the nucleus. During the interaction, the high-speed electrons have an electric field force F12 on the extra-nuclear electrons, and the extra-nuclear electrons have an electric field force F21 on the high-speed electrons.

Before collision:

First of all, according to Coulomb's law and the centripetal force equation, there is the Coulomb force of the positive electric field of the nuclear protons on the electrons outside the core before collision:

The gravitational force is very small compared to the Coulomb force, so it can be ignored.

According to these two equations, the product of the square of the velocity and the radius of the electrons outside the nucleus before the collision can be obtained:

Because of the uncertainty principle, v2 or r2 cannot be obtained, but can be obtained

. Both the electronic mass and the electronic charge have been accurately measured, so this value can be calculated quantitatively.

During collision:

At the next moment, the electrons move forward

At the same time, the speed decreases under the action of F21. The extranuclear electrons are displaced around the nuclear rotation line under the action of F2

At the same time, the speed increases under the action of F12. The trajectory of electrons is usually calculated based on the principle of constant light speed.

The energy change before and after this process can be obtained according to the law of conservation of energy. Let the electron outside the nucleus be the origin and the reference, then the kinetic energy Ek of the electron during the collision is converted into the potential energy Ep (in the electric field formed by the electron outside the nuclear) Ep and continuous X-ray energy Ex1:

After collision:

According to the law of conservation of energy, the electron outside the nucleus is still set as the origin and the reference, then the potential energy Ep of the electron is converted into kinetic energy after collision

The continuous X-ray energy Ex1 becomes a part of the radiant energy Er. If the electron makes a transition from an extranuclear electron out of orbit, the marked X-ray energy Ex2 becomes another part of the radiant energy:

Calculation of identification X-ray energy:

This part of the ray energy Ex2 is determined, and it is also related to the atomic number of the atom. Let the inner electron energy level energy E1 and the outer electron energy level energy E2 be the X-ray energy equal to

Marking X-rays are now widely used in the field of metal detection, and can theoretically be used to measure the composition of all materials except hydrogen H and helium He.

Calculation of continuous X-ray energy:

If the radius of rotation of the electrons around the core is determined, then the continuous X-ray energy Ex1 should be equal to

Using an electron gun to emit a high-speed electron beam, the electrons can generally be accelerated to about two-thirds the speed of light under the action of a high-voltage electric field. The distance r1 between the emitter of the electron and the electrons in the outer layer of the nucleus is much larger than the radius r2 of the electrons rotating around the nucleus. Therefore, the above formula should be a function of the radius of rotation of electrons around the core.

However, based on the continuous X-ray energy measured today, it seems difficult to say that a certain radius of electron rotation around the nucleus can be obtained. After all, it is because the current measurement methods can accurately measure the position of the electrons without affecting the speed of its rotation around the core; while accurately measuring the speed of the electrons' rotation around the core, they cannot affect its position.

That is to say, the position where the electrons outside the atom appear outside the nucleus is uncertain, or it is possible that the inside of the atom may be a model other than the planet model. With the advancement of measurement technology and the evolution of computing theory in the future, a conclusion may be drawn. This is also the research area of quantum mechanics.