Name: charged particle paths in magnetic fields
Uploaded: 2023-04-30T12:40:48.000Z
Duration: 1 min 22 s
Channel: JoVE

K12 Standards

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North Carolina K-12 Science Standard Course of Study

9-12

Physical Science

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Motion and Stability- Forces and Interactions

PS.PSc.6.4

motion-of-a-charged-particle-in-a-magnetic-field

Motion Of A Charged Particle In A Magnetic Field

Considere um ponto de massa m de carga Q movendo-se perpendicularmente a um campo magnético uniforme B.
A magnitude da força de Lorentz é constante e é sempre perpendicular à sua velocidade. Portanto, ele não pode alterar a magnitude da velocidade, apenas sua direção. Portanto, o caminho da partícula é um círculo com um raio r.
Usando a segunda lei do movimento de Newton, a força de Lorentz é igual à força centrípeta. Assim, o raio do círculo é calculado.
O período de tempo T do caminho circular da partícula é a circunferência por velocidade. Substituindo o valor de r, obtém-se T.
Se a velocidade não for perpendicular ao campo magnético, o componente paralelo ao campo magnético permanece inalterado, produzindo assim um movimento constante ao longo do campo magnético. Assim, a partícula se move em um caminho helicoidal.
Na fórmula do raio, o componente perpendicular da velocidade é substituído. Como T é independente da velocidade, ele permanece o mesmo.
Seu passo é definido como a distância entre voltas adjacentes, dada pelo produto do componente paralelo da velocidade e do período.

<ol>
	<li>OpenStax. (2019). Física Universitária Vol. 2. [Versão da Web], seção 11.3, páginas 501–506. Obtido de <a href="https://openstax.org/books/university-physics-volume-2/pages/11-3-motion-of-a-charged-particle-in-a-magnetic-field">Movimento de uma partícula carregada em um campo magnético</a></li>
</ol>

movimento de uma partícula carregada em um campo magnético

Uma partícula carregada sofre uma força ao se mover através de um campo magnético. Considere o campo como sendo uniforme e a partícula carregada movendo-se perpendicularmente a ele. Se o campo estiver em um vácuo, o campo magnético é o fator dominante que determina o movimento. Uma vez que a força magnética é perpendicular à direção do movimento, uma partícula carregada segue uma trajetória curva. A partícula continua a seguir essa trajetória curva até formar um círculo completo. Outra maneira de se observar isso é que a força magnética é sempre perpendicular à velocidade, de modo que ela não realiza trabalho sobre a partícula carregada. A energia cinética e a velocidade da partícula permanecem constantes. A força afeta a direção do movimento, mas não a magnitude da velocidade. Portanto, a partícula se move em um círculo. O tempo que a partícula leva para percorrer a trajetória circular é definido como período, que é o mesmo que a distância percorrida para fazer um ciclo completo, ou a circunferência do círculo, dividida pela velocidade.

Se a velocidade não for perpendicular ao campo magnético, então cada componente da velocidade precisa ser comparada separadamente com o campo magnético. A componente da velocidade perpendicular ao campo magnético produz uma força magnética perpendicular tanto a essa velocidade quanto ao campo. A componente paralela ao campo magnético cria um movimento constante na mesma direção do campo magnético. O movimento paralelo determina o passo da hélice, que é definido como a distância entre voltas adjacentes. Ele é igual à componente paralela da velocidade multiplicada pelo período. O resultado é um movimento helicoidal.

Enquanto a partícula carregada se desloca em uma trajetória helicoidal, ela pode entrar em uma região onde o campo magnético não é uniforme. Em particular, suponha que uma partícula se desloque de uma região com um campo magnético forte para uma região com um campo mais fraco, e depois volte para uma região com um campo mais forte. A partícula pode refletir antes de entrar na região com um campo magnético mais forte. Isso é semelhante a uma onda em uma corda que se desloca de uma corda muito leve e fina para uma parede dura e reflete para trás. Se a reflexão ocorre em ambas as extremidades, a partícula fica presa em um chamado "frasco magnético".

Movimento de uma Partícula Carregada em um Campo Magnético

Uma partícula carregada experimenta uma força ao se mover através de um campo magnético. Considere o campo uniforme e a partícula carregada para se mover ...

Education

JoVE Core

Physics

Física

Unit 1

Unidade 1

Magnetic Forces and Fields

Forças e Campos Magnéticos

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

charged particle paths in magnetic fields

A charged particle in a magnetic field follows a path that depends on the direction of its velocity. When the field is uniform and the particle moves perpendicular to it, the magnetic field is the main factor that controls the motion, especially in a vacuum. The magnetic force is always perpendicular to the direction of motion, so the particle curves into a circle.

Because the force stays perpendicular to velocity, it does no work on the particle. The kinetic energy and speed stay constant while the direction changes. The time for one full trip around the circle is the period, and it equals the circle’s circumference divided by the speed.

If the velocity is not perpendicular to the magnetic field, the motion must be split into two parts. The perpendicular component produces the magnetic force and causes circular motion. The parallel component keeps moving in the same direction as the magnetic field, so the particle follows a helical path.

In a helix, the pitch is the distance between neighboring turns. It is equal to the parallel velocity component multiplied by the period. A charged particle can also enter a region where the magnetic field is not uniform. If it moves from a strong field into a weaker one and then back toward a stronger field, it may reflect before reaching the stronger region again.

This reflection is similar to a wave on a string bouncing from a very light, thin string toward a hard wall. If the particle reflects at both ends, it becomes trapped in a magnetic bottle.

Charged Particle Paths in Magnetic Fields

charged-particle-paths-in-magnetic-fields

magnetism

Magnetic Poles and Everyday Uses

Magnetism appears in many everyday objects, from toys and hangers to elevators, doorbells, and computer devices. Magnets have two poles, called north and south. Like poles repel each other, while unlike poles attract. Both poles can also attract unmagnetized iron. A single magnetic pole cannot be isolated, because every part of a magnet contains both a north pole and a south pole. A compass needle is a simple example of a magnet. It is a thin bar magnet suspended at its center, so it can turn...

magnetic fields

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Magnetic force on moving charges depends on motion, charge, and field direction. A moving charge or a current creates a magnetic field in the space around it, along with its electric field. That magnetic field can then push on other moving charges or currents in the field. A magnetic field is a vector field, so it has direction as well as strength. At any point, the field direction is the direction a compass needle’s north pole points. The field strength is defined from the force a charged...

magnetic field lines

Reading Magnetic Field Lines

Magnetic field lines show the direction and strength of a magnetic field. They make it easier to picture how a magnet acts in space. Each line forms a closed loop around the magnet. For a bar magnet, the field lines leave the north pole and curve around to the south pole. They then continue through the magnet back to the north pole. This loop has no beginning or end. Magnetic field lines follow clear rules. The magnetic field points tangent to a field line at any point. A small compass points...

magnetic flux

Magnetic Flux Through Surfaces

Magnetic flux through a surface describes how much magnetic field passes across that surface. It is measured in weber (Wb), the SI unit for magnetic flux. Magnetic flux is a scalar quantity, not a vector. Three factors shape magnetic flux. They are the magnetic field strength B, the area the field crosses, and the orientation of the field relative to the surface. For a small area element dA, the flux depends on the part of the magnetic field that is normal, or perpendicular, to that element at...

motion of a charged particle in a magnetic field

A charged particle in a magnetic field follows a path that depends on the direction of its velocity. When the field is uniform and the particle moves perpendicular to it, the magnetic field is the main factor that controls the motion, especially in a vacuum. The magnetic force is always perpendicular to the direction of motion, so the particle curves into a circle. Because the force stays perpendicular to velocity, it does no work on the particle. The kinetic energy and speed stay constant...

magnetic force

Magnetic Fields and Moving Charges

Magnetic fields and moving charges create magnetic force. A moving electric charge, or a current made of many moving charges, produces a magnetic field. When another current or moving charge enters that field, it feels a magnetic force in response. At the atomic level, magnetic forces come from interactions between moving electrons in the atoms of two bodies. The strength of magnetic force depends on several factors. It increases with the size of the charge and with the strength of the...

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magnetic-force-on-a-current-carrying-conductor

Current and Magnetic Field Around a Wire

A current-carrying wire creates a magnetic field around it, and moving charges feel a force in that field. Because the magnetic field produced by moving charges is proportional to current, the wire itself acts as a source of magnetic field. A compass placed near the wire shows this effect by lining up tangentially around the wire. The magnetic field around a straight wire forms concentric circular loops. The right-hand rule helps determine the direction of those loops. If the thumb points in...

magnetic force on current-carrying wires: example

magnetic-force-on-current-carrying-wires-example

Balancing Weight with Magnetic Force

Magnetic force can balance the weight of a current-carrying wire when the wire sits in a magnetic field. Moving charges in the wire feel a force, so the wire itself can be pushed upward or downward. This example uses a flexible wire that is 40 cm long and has a mass of 10 g. It is held in a horizontal position inside a constant 0.40 T magnetic field. The goal is to find the current needed to remove the tension in the supporting leads. To do that, a free-body diagram is drawn first. The diagram...

force on a current loop in a magnetic field

force-on-a-current-loop-in-a-magnetic-field

Current Loops and Torque in Motors

Current loops in a magnetic field create the torque that drives a DC motor. A DC motor converts electrical energy into mechanical work. In a motor, wire loops sit inside a magnetic field. When current flows through the loops, the magnetic field pushes on them and makes the shaft rotate. The current is reversed when the loop lines up with the magnetic field. This keeps the torque on the loop going in the same direction. A commutator and brushes handle this reversal. The commutator switches the...

torque on a current loop in a magnetic field

torque-on-a-current-loop-in-a-magnetic-field

Current Loop Torque in Electric Motors

Current loop torque in electric motors shows how magnetic force can make a wire loop rotate. In an electric motor, loops of wire sit between magnets in a magnetic field. When current flows through the loops, the field applies torque. This rotation turns a shaft and converts electrical energy into mechanical energy. A rectangular current-carrying loop with N turns in a uniform magnetic field has zero net force. Even so, it can still experience net torque. The torque depends on the current I,...

the hall effect

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thomson's e/m experiment

Electron Speed Selector in Thomson’s Tube

A velocity selector uses electric and magnetic fields to choose charged particles with one speed from a beam. Many beams from a heated cathode contain particles moving at different speeds, so this setup helps produce a uniform beam. The electric and magnetic fields are perpendicular to the particle’s motion and to each other. In this arrangement, a particle with charge q, speed v, and mass m enters from the top. The magnetic field points into the plane of the paper, and the electric field...

key terms and concepts

Explore how charged particles move in magnetic fields, from circular motion to helical paths and magnetic bottles, with clear high school physics terms.

Charged Particle Paths in Magnetic Fields | JoVE K12

physics

JoVE Core - Fisica apresenta a teoria e a aplicação de tópicos fundamentais da física, incluindo cinemática, dinâmica, mecânica dos fluidos, estática, ondas e acústica, com vídeos animados concisos e de fácil compreensão. Além disso, os vídeos de cientistas em ação demonstram a aplicação de conceitos relacionados em experimentos de pesquisa clássica e original realizados nos laboratórios de todo o mundo hoje em dia.

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Ohio’s Learning Standards and Model Curriculum

Electricity And Magnetism

Electromagnetic interactions

Tennessee Academic Standards

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Energy

PHYS.PS3.9

Virginia  Standards of Learning

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PS.9

PS.9.d

PH.7

PH.7.a

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Minnesota Academic Standards in Science

3.1.1 9P.2.2.1.3

Arizona Science Standards

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HS.P2U1.5

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Waves and Their Applications in Technologies for Information Transfer

9-12.PS.2.3.b

Next Generation Science Standards

Motion and Stability: Forces and Interactions

HS-PS2-4

HS-PS2-5

Florida Department of Education

SC.912.P.10

SC.912.P.10.16

Texas Essential Knowledge and Skills

PHYS.6

PHYS.6.B

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New York State Science Learning Standards

HS. Forces and Interactions

HS-PS2-5.

HS. Energy

HS-PS3-5.

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Charged Particle Paths in Magnetic Fields

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