The motion of charged particles in an electric field in a magnetic field

The first question is that you don't need to think about the closed loop.

The condition for the two particles to move in a uniform circular motion in the q field is that the force of the positive charge of the electric quantity q to the negative charged particles emitted from the electron gun is equal to the centripetal force, that is, f=kqq r 2=mv 2 r, where v is the velocity of the negative charge ejecting from point o after acceleration.

If the electron gun is required to emit particles at this velocity, the energy in it is converted to qu=(mv2)2.

After combining the two formulas, we get u=kq 2r, and it can be found that the magnitude of u is not related to the amount of electricity and mass of the emitted particles.

Since there is no diagram in the second question, I can only answer as follows.

When the particle can move in a uniform circular motion, the accelerating voltage of the electron emission gun must meet the condition of the previous question, that is, a fixed value, which is also the terminal voltage of the resistor RO in the loop. Since the electron accelerator gun is equivalent to a capacitor, the terminal voltage of the RO can be calculated in the closed loop without considering the influence of the electron accelerator gun on the circuit, as if it is not connected to the circuit. You can judge the change of the voltage at the RO terminal based on whether the left and right movement of the sliding rheostat increases or decreases, and it is also the change of the U in the electron accelerator gun.

When the R0 voltage increases, U also increases, resulting in a larger velocity of the particles emitted at point O, and the trajectory should be a spiral with a gradually increasing radius, and vice versa.

Characteristics of the motion of charged particles in a uniform magnetic field.

If the velocity direction of the charged particle is parallel to the direction of the magnetic induction intensity, the charged particle will not be subjected to the Lorentz force and will move in a uniform linear velocity.

If the velocity direction of the charged particle is perpendicular to the direction of magnetic induction, the charged particle will be subjected to the Lorentz force, and the direction of the Lorentz force will always be perpendicular to the direction of velocity, and the charged particle will move in a uniform circular motion, and the centripetal force will be provided by the Lorentz force. (The uniform circular motion of charged particles in a uniform magnetic field is the focus and difficulty of the exam).

If the velocity direction of the charged particle is neither parallel nor perpendicular to the direction of the magnetic induction, the charged particle will make a spiral motion in the magnetic field.

The charged particles move in a uniform circular motion in a uniform magnetic field.

Law of motion: The Lorentz force provides the centripetal force needed to do uniform circular motion.

The centripetal f-direction = mv r required for the charged particles to move in a uniform circular motion has the f-direction = bvq.

Charged particles: In physics, refers to particles that have an electric charge. It can be a subatomic particle or an ion.

A mass of charged particles, or a gas with a certain percentage of charged particles, is called plasma. The plasma state is the fourth state of matter because its properties are different from those of solids, liquids, and gases. Particles can be positively charged, negatively charged, or uncharged (neutral).

Charged particles move in a uniform circular motion in a uniform magnetic field, which is a relatively common form of motion.

If the velocity direction of the charged particle is perpendicular to the direction of the magnetic induction, the charged particle will be affected by the Lorentz force, and the direction of the Lorentz force will always be perpendicular to the direction of velocity, the charged particle will move in a uniform circular motion, the centripetal force is provided by the Lorentz force, and the uniform circular motion of the charged particles in a uniform magnetic field is the focus and difficulty of the exam.

Characteristics of the motion of charged particles in a magnetic field:

The motion of charged particles in a magnetic field is often complex, and we only consider a few of these special cases: the gravitational force of the particles themselves is not considered (generally, electrons, protons, particles, ions, etc. do not consider their gravity); The magnetic field is a uniform magnetic field.

The initial velocity v0 is parallel to the magnetic field: at this time the Lorentz force f 0 and the particle will move in a uniform straight line along the direction of the initial velocity.

The initial velocity is perpendicular to the magnetic field: since the Lorentz force is always perpendicular to the direction of motion of the particle, the particle moves in a uniform circular motion under the action of the Lorentz force, and its centripetal force is provided by the Lorentz force, so its orbital radius is and the period of motion is.

It can be seen that particles with the same charge-to-mass ratio enter the same magnetic field at the same velocity, and their orbital radius is the same; Particles with the same charge enter the same magnetic field with the same momentum and have the same radius of their orbits. The period t of their motion has nothing to do with the velocity of the particle, independent of the orbital radius r of the particle, as long as it is a particle with the same charge-to-mass ratio and enters the same magnetic field, its period is the same.

Motion of charged particles in an electric field:The conditions for whether the gravitational force of a charged particle is negligible are as follows:

1) Elementary particles.

Such as electrons, protons, particles, ions, etc., without an explanation or explicit hint, gravity is generally not counted. The motion of charged particles in an electric field generally does not consider the gravitational force of the particles There are two situations in which charged particles move in an electric field: the second case is that the charged particles follow the electric field lines.

Enter the electric field and move in a straight line.

2) Charged particles: such as dust, liquid droplets, oil droplets, small balls, etc., if there is no explanation or clear hint, gravity should generally be considered; In the electric field, it is subjected to the force of the electric field.

gravity, elasticity, friction force.

by Newton's second law.

to determine its state of motion, so this part of the problem will involve the knowledge of dynamics and kinematics in mechanics.

3) Gravity is generally taken into account when it comes to balancing.

Linear acceleration of charged particles:

1) Motion state analysis: the charged particles enter the uniform electric field in the direction parallel to the direction of the electric field line, and the electric field force and the direction of motion are in the same straight line, and the uniform speed (decrease) linear motion is done.

2) Analysis from a functional point of view: particles are only affected by the electric field force, and the electric field force does the work.

That is, the work is done by the combined external force, so the change in the kinetic energy of the particle is equal to the change in the electric potential energy.

1. Velocity deflection angle =Rounded cornerso = 2 timesChord chamfering

2. The particles that are injected in the direction of the radius will come out in the direction of the radius. To put it simply: [radial in, radial out].

The three scattered reeds are the longest and shortest in the comparative magnetic field.

Gardens of the same size, arc length.

The longer, the longer. Within a semicircle, the longer the arc length, the longer the chord.

The longer it is, the bigger the central corner!

Magnetically focused, when the radius r of the trajectory circle and the radius r of the magnetic field circle are the same, the particles entering parallel to each other, after passing through the magnetic field, converge into a focal point. The reverse is also true. At the same time, it can be concluded that:

The velocity v is perpendicular to the diameter of the overfocus. The shape enclosed by the center and intersection point of the two digging beam circles is diamond-shaped.

Fourth, the problem of rotating circles.

A circle of the same size rotates around a point above the circle, and the center of the circle is on a circle. It is equivalent to the radius rotating around a point.

Scale the circle. The velocity is tangent.

Draw circles of different sizes.

The motion of charged particles in a magnetic field is a gyratory motion.

The cyclotron gyration of a charged particle in a magnetic field refers to the uniform circular motion of charged particles around the magnetic field lines in a constant magnetic field.

A particle with a quantity of q, a mass of m, and a velocity v is subjected to the Lorentz force f=qv b when moving in a uniform and constant magnetic field b, and the direction of the force f is perpendicular to the direction of velocity v and magnetic field b, and the value is qv b, and v is the component of velocity v perpendicular to the direction of the magnetic field. This force can only change the direction of the velocity, not the value of the velocity. Also known as gyro or lamor motion.

Principle

The frequency at which the particle rotates around the magnetic field lines. This is called the gyration frequency or Lamor frequency. The direction of the gyratory motion is related to the positive and negative signs of the charge carried by the particle.

For a definite particle, the stronger the magnetic field, the higher the cyclotron frequency; The greater the mass, the smaller the maneuver frequency. The trajectory of the gyratory motion is a circle, which is called the Lamor circle.

As can be seen from the formula, if two particles with the same charge but different masses have the same velocity and the same magnetic field, the Lamor radius is proportional to the mass of the particle. This principle is often used to make mass spectrometry instruments. For charged particles with a certain velocity, the stronger the magnetic field, the smaller the Lamor radius.

Therefore, with a strong enough magnetic field, it is possible to confine charged particles around the magnetic field lines.

The motion of charged particles in a magnetic field is a uniform circular motion. The gyratory motion of charged particles refers to the uniform circular motion of charged particles around the magnetic field lines in a constant magnetic field. A particle with an electric quantity of q, a mass of m, and a velocity friend base of v is subject to the Lorentz force when moving in a uniform and constant magnetic field b.

Characteristics of the movement of charged particles

The frequency at which the particle rotates around the magnetic field lines. This is called the gyration frequency or Lamor frequency. The direction of the gyratory motion is related to the positive and negative signs of the charge carried by the particle.

For a definite particle, the stronger the magnetic field, the higher the cyclotron frequency; The greater the mass, the smaller the gyro frequency. The trajectory of the gyratory motion is a circle, which is called the Lamor circle.

The charged particles in the magnetic field move in a circular motion around the magnetic field lines, and they form small rings of electric current, and the direction of rotation of the positive and negative charges is opposite, but the direction of the current formed is the same. The total effect of the whirling motion of a large number of charged particles around the magnetic field lines is the formation of a hoop current.

This current can produce an induced magnetic field, the direction of which is exactly opposite to the original magnetic field b, and it plays the role of counteracting or resisting the original magnetic field, this property is called diamagnetism, so the plasma can be regarded as a magnetic medium.

The movement of charged particles in a magnetic field has a wide range of applications, and here are a few common examples:

1.Particle accelerator: Charged particles are subjected to a force in a magnetic field and can be used to accelerate the motion of particles. Accelerators are widely used in high-energy physics research, such as exploring the structure and properties of elementary particles.

2.Magnetic Resonance Imaging (MRI): MRI uses the movement of charged particles in a strong magnetic field to produce images.

By applying a reinforced magnetic field to the subject and applying a ladder cavity magnetic field around it, signals from different tissues can be obtained, resulting in high-resolution images of the internal structure.

3.Magnetometers and Hall-effect sensors: When charged particles move in a magnetic field, a magnetic field effect is generated.

Magnetometers and Hall effect sensors use this principle to measure the magnitude and direction of magnetic fields, and are widely used in navigation, position detection, current measurement and other fields.

4.Electron Beam Welding and Electron Beam Etching: By applying a magnetic field to the charged particle beam of Nachaipe, the path of the particle beam can be precisely controlled, enabling high-precision welding and etching. This technology has important applications in microelectronics manufacturing, material processing, and other fields.

In general, the application of charged particles moving in a magnetic field covers many fields, including basic scientific research, medical diagnosis, sensing technology, and materials processing.

1.Particle accelerators: Particle accelerators use magnetic fields to guide and accelerate charged particles to very high energies. These accelerators are widely used in scientific research fields such as nuclear physics, particle physics, etc.

2.Magnetic Resonance Imaging (MRI): The MRI technique commonly used in medicine makes use of the movement of charged particles in a magnetic field.

A strong and uniform magnetic field orients the charged nuclei in the body, and by measuring the resulting signals, high-quality images of the body can be generated for diagnosis and research.

3.Magnetic sensors: Charged particles are subjected to magnetic forces when they move in a magnetic field, and this principle is used in the design and manufacture of magnetic field sensors. Magnetic sensors are widely used in navigation, measurement, automation, and other fields to detect and measure the magnetic field around an object.

4.Ion implantation: Ion implantation technology uses a magnetic field to direct charged particles to a specific location, and the Hunger Cavity enables the injection of ions into a material to change its carrying properties and properties. This technology has important applications in semiconductor processing, material modification and other fields.

5.Particle detectors: Magnetic fields can be used to design and build particle detectors that are used to detect and measure the motion and properties of charged particles.

For example, detectors on electron accelerators can be used to detect cosmic rays, and particle detectors are also needed for experiments in research projects such as the Large Hadron Collider on Earth.

6.Ferrofluid sealing: Magnetic fields can be used to achieve ferrofluid sealing, which can be used to seal liquids and gases by taking advantage of the motion characteristics of charged particles in a magnetic field. This technology is widely used in machinery and equipment, chemical industry and other fields, and rot can improve the tightness and reliability of equipment.