Motion of charged particles in a magnetic field 15

1. Motion of charged particles in a uniform magnetic field

1. Determination of the center of the circle: According to the characteristics of the circular motion, it can be known that the center of the circle must be in a straight line perpendicular to the velocity, and must be on the perpendicular line of a string in the circle.

2. Determination and calculation of radius: the radius can be determined by using the knowledge of plane geometry.

3. Calculation of the motion time of particles in the magnetic field: the time of the movement of particles in the magnetic field can be obtained according to the geometric relationship and the relationship between the tangent angle and the central angle of the circle.

2. Motion of charged particles in a composite field:

A composite field is a field in which an electric field, a magnetic field, and a gravitational field coexist in the same space, or two fields coexist. Charged particles may be subjected to several forces of different properties at the same time as they move in these composite fields.

When a charged particle moves in a composite field, as long as the gravitational electric field force does work on it, its kinetic energy will change; But the Lorentz force is not work, it only changes the direction of motion and does not change the magnitude of the velocity of motion.

There are many types of motion of charged particles in a composite field, and the common ones are as follows:

1. When the resultant external force of the charged particles in the composite field is zero, the particles will be at rest or move in a uniform linear motion.

2. When the resultant external force of the charged particle is directed to the center of a circle as a centripetal force, the particle will move in a uniform circular motion (for example, the electric field force and gravity are balanced, and the Lorentz force provides the centripetal force).

3. When the magnitude and direction of the resultant external force on the charged particles are constantly changing, the particles will move in a curve at a non-uniform variable speed.

4. The movement of charged particles under the constraints of insulating rods or insulated wires.

Finding the center of the circle is generally found with the velocity of two points. We know that the intersection of any two radii is the center of the circle, and the velocity is perpendicular to the radius in the tangential direction, if we know the direction of the two velocities, then the intersection of the two straight lines perpendicular to the velocity is the center of the circle.

The above is the most common type of problem to find the center of the circle, if you know the two points on the trajectory and the length of the radius, then the center of the circle is easier to find. Take two points as the center of the circle, and the radius as the radius to make a circle, and one of the intersection points is the center of the orbital circle.

Supplement: 1. The center of the circle is determined by the perpendicular line of two speeds.

2. The center of the circle is determined by the perpendicular bisector of the two strings.

3. The center of the circle is determined by the extension wire of the two Lorentz forces.

Fourth, the comprehensive centering of the circle.

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.

The motion of charged particles in a uniform magnetic field is as follows.

Uniform linear motion.

When v b, the charged particles move in a uniform straight line with velocity v.

Uniform circular motion.

When v b, the charged particles are perpendicular to the magnetic inductance line.

The plane moves in a uniform circular motion with the incident velocity.

Problems with the motion of charged particles.

1. Acceleration problem in electric field.

Charged particles are only subjected to the electric field force in the electric field.

role of the problem. If in a uniform electric field, the problem can be solved according to Newton's laws of motion.

Combined with kinematic formulas or kinetic energy theorems.

Differential line processing. However, the problem in the non-uniform electric field can only be solved according to the kinetic energy theorem.

2. Deflection in the electric field.

The charged particles enter the electric field at a certain speed and at a certain angle to the electric field, so that the direction of force of the charged particles is not in the same straight line as the direction of velocity, and the particles will move in a curve.

It is common for charged particles to be injected into the electric field in the direction of the perpendicular electric field, and the analysis method of this kind of problem is the same as the analysis method of the flat motion problem, which decomposes the motion of the particle into a uniform acceleration motion along the direction of force and a uniform motion in the direction of initial velocity. The main problems to be solved are the terminal velocity, deflection distance, and deflection angle of charged particles.

3. Deflection in magnetic fields.

A charged particle that is injected into a magnetic field, as long as its velocity direction is at an angle to the magnetic field. It is subjected to the Lorentz force of the magnetic field on it.

Function. If a charged particle is injected perpendicularly into a uniform magnetic field, the direction of its initial velocity and the direction of the Lorentz force are in a plane perpendicular to the direction of the magnetic field, and there is no action to cause the particle to leave this plane, so the particle can only move in this plane.

4. Motion problems in composite fields.

The so-called motion in a composite field is the problem of motion in two or more fields. Charged particles are subjected to two or more forces in a composite field, and the motion is generally complex and difficult to solve in high school. However, it is possible to design the problem of uniform motion of particles or uniform circular motion of particles.

The solution is to analyze the force and judge the unknown quantity according to the motion characteristics of the particles.

Charged particles are made in a uniform magnetic fieldUniform circumference with late filial piety movement

If the velocity direction of the charged particle is related to the magnetic induction intensity.

The direction is perpendicular and the charged particles will be subjected to the Lorentz force.

and the direction of the Lorentz force is always perpendicular to the direction of velocity, and the charged particles will move in a uniform circular motion, centripetal force.

Courtesy of Lorentz Force.

The motion of charged particles in a magnetic field.

1. Parallel magnetic field entry (V b).

The motion of the charged particles in the magnetic field enters in parallel and is not affected by the Lorentz force, and the particles move in a uniform linear motion.

2. Vertical magnetic field entry (V b).

The Lorentz force is always perpendicular to the velocity and acts as a centripetal force, moving in a uniform circular motion under the action of the Lorentz force. r=mv is obtained from qvb=mv r (centripetal force provided by the Lorentz force) and t=2 m qb or t=2 r v is obtained from qvb=m(2 t) r.

3. It is neither perpendicular nor parallel to the magnetic field.

Decompose the velocity into the direction along the magnetic field and the direction perpendicular to the magnetic field. The velocity component in the direction of the parallel magnetic field is v = v·sin, and the velocity component in the direction of the perpendicular magnetic field is v = v·cos.

The motion of charged particles in a uniform magnetic field isUniform circular motion.

When the direction of the charge velocity is delayed and perpendicular to the direction of the magnetic field, the Lorentz force.

size f=bvq; When the angle between the direction of charge motion and the direction of the magnetic field is 0, the magnitude of the Lorentz force is f=bvqsine; The most important characteristic of the Lorentz force is that the magnitude is related to the velocity.

The magnetic field has no force on the stationary charge, and the magnetic field only has an action on the moving charge, which is similar to the electric field always having an electric field force on the stationary charge or the moving charge in it.

The role is different.

The direction of the Lorentz force is always perpendicular to the direction of the velocity of the motion and can be obtained by the left-handed rule.

to judge. Charged particles act as a centripetal force under the action of the Lorentz force and can do a uniform circular motion.

General solution ideas for the motion of charged particles in a uniform magnetic field.

1. Clarify the trajectory. The motion of charged particles is a circular motion, and students need to determine the trajectory of the movement first. Some questions don't clearly tell you the trajectory, you need to analyze it yourself, draw it yourself, and sometimes you have to revise it after you draw it.

2. Find the center of the circle. After determining the approximate trajectory of motion, we began to study the center of the circle. The center of the circle is generally the perpendicular line of the velocity of two points.

Intersection. 3. Construct a suitable triangle. Combined with the subject conditions, a right-angled triangle is constructed.

and in it expresses the deflection radius r; In general, a lot of geometry knowledge is used.

4. Combined with the physical formula of the deflection radius. Once you have a radius r, combine the above physical formula R=mv bq.

The above information reference: Encyclopedia - Uniform Magnetic Field.

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.