Application of the Lorentz force in nature. Lorentz force
DEFINITION
Lorentz force– the force acting on a point charged particle moving in a magnetic field.
It is equal to the product of charge, particle velocity modulus, induction vector modulus magnetic field and the sine of the angle between the magnetic field vector and the speed of the particle.
Here is the Lorentz force, is the particle charge, is the magnitude of the magnetic field induction vector, is the particle velocity, is the angle between the magnetic field induction vector and the direction of motion.
Unit of force – N (newton).
The Lorentz force is a vector quantity. The Lorentz force takes its toll highest value when the induction vectors and direction of the particle velocity are perpendicular ().
The direction of the Lorentz force is determined by the left-hand rule:
If the magnetic induction vector enters the palm of the left hand and four fingers are extended towards the direction of the current movement vector, then the thumb bent to the side shows the direction of the Lorentz force.
In a uniform magnetic field, the particle will move in a circle, and the Lorentz force will be a centripetal force. In this case, no work will be done.
Examples of solving problems on the topic “Lorentz force”
EXAMPLE 1
EXAMPLE 2
Exercise | Under the influence of the Lorentz force, a particle of mass m with charge q moves in a circle. The magnetic field is uniform, its strength is equal to B. Find centripetal acceleration particles. |
Solution | Let us recall the Lorentz force formula: In addition, according to Newton's 2nd law: In this case, the Lorentz force is directed towards the center of the circle and the acceleration created by it is directed there, that is, this is centripetal acceleration. Means: |
Along with the Ampere force, Coulomb interaction, and electromagnetic fields, the concept of Lorentz force is often encountered in physics. This phenomenon is one of the fundamental ones in electrical engineering and electronics, along with, and others. It affects charges that move in a magnetic field. In this article we will briefly and clearly examine what the Lorentz force is and where it is applied.
Definition
When electrons move along a conductor, a magnetic field appears around it. At the same time, if you place a conductor in a transverse magnetic field and move it, an electromagnetic induction emf will arise. If a current flows through a conductor located in a magnetic field, the Ampere force acts on it.
Its value depends on the flowing current, the length of the conductor, the magnitude of the magnetic induction vector and the sine of the angle between the magnetic field lines and the conductor. It is calculated using the formula:
The force under consideration is partly similar to that discussed above, but it acts not on a conductor, but on a moving charged particle in a magnetic field. The formula looks like:
Important! The Lorentz force (Fl) acts on an electron moving in a magnetic field, and on a conductor - Ampere.
From the two formulas it is clear that in both the first and second cases, the closer the sine of the angle alpha is to 90 degrees, the greater the effect on the conductor or charge by Fa or Fl, respectively.
So, the Lorentz force characterizes not the change in velocity, but the effect of the magnetic field on a charged electron or positive ion. When exposed to them, Fl does not do any work. Accordingly, it is the direction of the charged particle’s velocity that changes, and not its magnitude.
As for the unit of measurement of the Lorentz force, as in the case of other forces in physics, such a quantity as Newton is used. Its components:
How is the Lorentz force directed?
To determine the direction of the Lorentz force, as with the Ampere force, the left-hand rule works. This means, in order to understand where the Fl value is directed, you need to open the palm of your left hand so that the lines of magnetic induction enter your hand, and the extended four fingers indicate the direction of the velocity vector. Then the thumb, bent at a right angle to the palm, indicates the direction of the Lorentz force. In the picture below you can see how to determine the direction.
Attention! The direction of the Lorentz action is perpendicular to the particle motion and the magnetic induction lines.
In this case, to be more precise, for positively and negatively charged particles the direction of the four unfolded fingers matters. The left-hand rule described above is formulated for a positive particle. If it is negatively charged, then the lines of magnetic induction should be directed not towards the open palm, but towards its back, and the direction of the vector Fl will be the opposite.
Now we will tell in simple words, what this phenomenon gives us and what real impact it has on the charges. Let us assume that the electron moves in a plane perpendicular to the direction of the magnetic induction lines. We have already mentioned that Fl does not affect the speed, but only changes the direction of particle movement. Then the Lorentz force will have a centripetal effect. This is reflected in the figure below.
Application
Of all the areas where the Lorentz force is used, one of the largest is the movement of particles in the earth's magnetic field. If we consider our planet as a large magnet, then the particles that are located near the northern magnetic poles, make an accelerated movement in a spiral. As a result, they collide with atoms from the upper atmosphere, and we see the northern lights.
However, there are other cases where this phenomenon applies. For example:
- Cathode ray tubes. In their electromagnetic deflection systems. CRTs have been used for more than 50 years in a row in various devices, ranging from the simplest oscilloscope to televisions different forms and sizes. It is curious that when it comes to color reproduction and working with graphics, some still use CRT monitors.
- Electrical machines – generators and motors. Although the Ampere force is more likely to act here. But these quantities can be considered as adjacent. However, these are complex devices during operation of which the influence of many physical phenomena is observed.
- In accelerators of charged particles in order to set their orbits and directions.
Conclusion
Let us summarize and outline the four main points of this article in simple language:
- The Lorentz force acts on charged particles that move in a magnetic field. This follows from the basic formula.
- It is directly proportional to the speed of the charged particle and magnetic induction.
- Does not affect particle speed.
- Affects the direction of the particle.
Its role is quite large in the “electrical” areas. The specialist should not lose sight of the basic theoretical information about the fundamental physical laws. This knowledge will be useful, as well as for those who deal scientific work, design and just for general development.
Now you know what the Lorentz force is, what it is equal to and how it acts on charged particles. If you have any questions, ask them in the comments below the article!
Materials
The Lorentz force is a force that acts from electromagnetic field on a moving electric charge. Quite often, only the magnetic component of this field is called the Lorentz force. Formula to determine:
F = q(E+vB),
Where q— particle charge;E— electric field strength;B— magnetic field induction;v— particle speed.
The Lorentz force is very similar in principle to, the difference is that the latter acts on the entire conductor, which is generally electrically neutral, and The Lorentz force describes the influence of the electromagnetic field only for a single moving charge.
It is characterized by the fact that it does not change the speed of movement of charges, but only affects the velocity vector, that is, it is capable of changing the direction of movement of charged particles.
In nature, the Lorentz force allows us to protect the Earth from the effects of cosmic radiation. Under its influence, charged particles falling on the planet deviate from a straight trajectory due to the presence of the Earth's magnetic field, causing auroras.
In technology, the Lorentz force is used very often: in all engines and generators it is this that drives the rotor under the influence of the electromagnetic field of the stator.
Thus, in any electric motors and electric drives the main type of force is Lorentzian. In addition, it is used in charged particle accelerators, as well as in electron guns, which were previously installed in tube televisions. In a kinescope, electrons emitted by a gun are deflected under the influence of an electromagnetic field, which occurs with the participation of the Lorentz force.
Additionally, this force is used in mass spectrometry and mass electrography for instruments that can sort charged particles based on their specific charge (the ratio of charge to particle mass). This makes it possible to determine the mass of particles with high accuracy. It also finds application in other instrumentation, for example, in a non-contact method for measuring the flow of electrically conductive liquid media (flow meters). This is very important if the liquid medium has very high temperature(melt of metals, glass, etc.).
In the article we will talk about the Lorentz magnetic force, how it acts on a conductor, consider the left-hand rule for the Lorentz force and the moment of force acting on a current-carrying circuit.
The Lorentz force is a force that acts on a charged particle falling at a certain speed into a magnetic field. The magnitude of this force depends on the magnitude of the magnetic induction of the magnetic field B, electric charge of the particle q and speed v, from which the particle falls into the field.
The way a magnetic field B behaves in relation to the load completely different from how it is observed for the electric field E. First of all, the field B does not respond to load. However, when the load moves into the field B, a force appears, which is expressed by a formula that can be considered as a definition of the field B:
Thus, it is clear that the field B acts as a force perpendicular to the direction of the velocity vector V loads and vector direction B. This can be illustrated in a diagram:
In the diagram q has a positive charge!
The units of the B field can be obtained from the Lorentz equation. Thus, in the SI system, the unit B is equal to 1 tesla (1T). In the CGS system, the field unit is Gauss (1G). 1T = 10 4 G
For comparison, an animation of the movement of both positive and negative charges is shown.
When the field B covers large area, charge q moving perpendicular to the direction of the vector B, stabilizes its movement along a circular path. However, when the vector v has a component parallel to the vector B, then the charge path will be a spiral as shown in the animation
Lorentz force on a current-carrying conductor
The force acting on a current-carrying conductor is the result of the Lorentz force acting on moving charge carriers, electrons or ions. If the guide section has a length l, as in the drawing
the total charge Q is moving, then the force F acting on this segment is
The quotient Q / t is the value of the flowing current I and, therefore, the force acting on the section with the current is expressed by the formula
To take into account the dependence of the force F from the angle between the vector B and the axis of the segment, length of the segment l was given by the characteristics of the vector.
Only electrons move in the metal under the influence of potential differences; metal ions remain immobile in the crystal lattice. In electrolyte solutions, anions and cations are mobile.
Left hand rule Lorentz force— determining the direction and return of the vector of magnetic (electrodynamic) energy.
If the left hand is positioned so that the magnetic field lines are directed perpendicular to the inner surface of the hand (so that they penetrate into the hand), and all fingers - except the thumb - point in the direction of positive current flow (moving molecule), the deflected thumb indicates the direction of the electrodynamic force acting to a positive electric charge placed in this field (for a negative charge, the force will be the opposite).
The second way to determine the direction of the electromagnetic force is to position the thumb, index and middle fingers at right angles. With this arrangement index finger shows the direction of magnetic field lines, the direction of the middle finger is the direction of current flow, and also the direction of the thumb of force.
Moment of force acting on a current-carrying circuit in a magnetic field
The moment of force acting on a circuit with current in a magnetic field (for example, on a wire coil in the winding of an electric motor) is also determined by the Lorentz force. If the loop (marked in red in the diagram) can rotate around an axis perpendicular to the field B and conducts a current I, then two unbalanced forces F appear acting to the sides of the frame parallel to the axis of rotation.