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

Consideremos una masa puntual m de carga Q que se mueve perpendicularmente a un campo magnético uniforme B.
La magnitud de la fuerza de Lorentz es constante y siempre es perpendicular a su velocidad. Por lo tanto, no puede cambiar la magnitud de la velocidad, solo su dirección. Por lo tanto, la trayectoria de la partícula es un círculo con un radio r.
Usando la segunda ley del movimiento de Newton, la fuerza de Lorentz es igual a la fuerza centrípeta. Por lo tanto, se calcula el radio del círculo.
El período de tiempo T de la trayectoria circular de la partícula es la circunferencia por la velocidad. Sustituyendo el valor de r, se obtiene T.
Si la velocidad no es perpendicular al campo magnético, el componente paralelo al campo magnético no se ve afectado, produciendo así un movimiento constante a lo largo del campo magnético. Por lo tanto, la partícula se mueve en una trayectoria helicoidal.
En la fórmula del radio, se sustituye la componente perpendicular de la velocidad. Dado que T es independiente de la velocidad, sigue siendo la misma.
Su paso se define como la distancia entre vueltas adyacentes, dada por el producto de la componente paralela de la velocidad y el período.

<ol>
	<li>OpenStax. (2019). Física Universitaria Vol. 2. [Versión web], sección 11.3, páginas 501–506. Obtenido de <a href="https://openstax.org/books/university-physics-volume-2/pages/11-3-motion-of-a-charged-particle-in-a-magnetic-field">Movimiento de una partícula cargada en un campo magnético</a></li>
</ol>

movimiento de una partícula cargada en un campo magnético.

Una partícula cargada experimenta una fuerza al moverse a través de un campo magnético. Consideremos que el campo es uniforme y que la partícula cargada se mueve perpendicular a él. Si el campo está en el vacío, el campo magnético es el factor dominante que determina el movimiento. Dado que la fuerza magnética es perpendicular a la dirección del movimiento, una partícula cargada sigue una trayectoria curva. La partícula continúa siguiendo esta trayectoria curva hasta que forma un círculo completo. Otra manera de ver esto es que la fuerza magnética siempre es perpendicular a la velocidad, por lo que no realiza trabajo sobre la partícula cargada. La energía cinética y la velocidad de la partícula se mantienen constantes. La fuerza afecta la dirección del movimiento pero no la velocidad. Por lo tanto, la partícula se mueve en un círculo. El tiempo que tarda la partícula cargada en dar la vuelta alrededor de la trayectoria circular se define como el período, que es igual a la distancia recorrida para completar un ciclo completo o la circunferencia del círculo dividida por la velocidad. Si la velocidad no es perpendicular al campo magnético, entonces cada componente de la velocidad necesita ser comparada por separado con el campo magnético. La componente de la velocidad perpendicular al campo magnético produce una fuerza magnética perpendicular tanto a esta velocidad como al campo. La componente paralela al campo magnético crea un movimiento constante en la misma dirección que el campo magnético. El movimiento paralelo determina el paso de la hélice, que se define como la distancia entre vueltas adyacentes. Es igual a la componente paralela de la velocidad multiplicada por el período. El resultado es un movimiento helicoidal. Mientras la partícula cargada viaja en una trayectoria helicoidal, puede ingresar a una región donde el campo magnético no es uniforme. En particular, supongamos que una partícula viaja desde una región de campo magnético fuerte a una región de campo más débil, luego vuelve a una región de campo más fuerte. La partícula puede reflejarse antes de ingresar a la región de campo magnético más fuerte. Esto es similar a una onda en una cuerda que viaja desde una cuerda muy liviana y delgada hacia una pared dura y se refleja hacia atrás. Si la reflexión ocurre en ambos extremos, la partícula queda atrapada en lo que se llama una "botella magnética".

Movimiento de una partícula cargada en un campo magnético.

Una partícula cargada experimenta una fuerza cuando se mueve a través de un campo magnético. Considere que el campo es uniforme y que la partícula cargada se mueve ...

Education

Educación

JoVE Core

Physics

Física

Unit 1

Unidad 1

Magnetic Forces and Fields

Fuerzas y campos magnéticos

KEY TERMS AND CONCEPTS

TÉRMINOS Y CONCEPTOS CLAVE

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...

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Reading Magnetic Field Lines

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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...

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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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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...

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

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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...

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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,...

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thomson's e/m experiment

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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

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JoVE Core Física presenta la teoría y la aplicación de conceptos físicos fundamentales, como la cinemática, dinámica, mecánica de fluidos, estática, ondas y acústica, mediante animaciones audiovisuales concisas y fáciles de entender. Además, los vídeos de científicos en acción muestran la aplicación de los conceptos relacionados en experimentos de investigación clásicos y originales, realizados en laboratorios de todo el mundo.

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Ohio’s Learning Standards and Model Curriculum

Electricity And Magnetism

Electromagnetic interactions

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PHYS.PS3.9

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PS.9

PS.9.d

PH.7

PH.7.a

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HS.P2U1.5

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Waves and Their Applications in Technologies for Information Transfer

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Next Generation Science Standards

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Florida Department of Education

SC.912.P.10

SC.912.P.10.16

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PHYS.6

PHYS.6.B

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New York State Science Learning Standards

HS. Forces and Interactions

HS-PS2-5.

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Resistivity

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Charged Particle Paths in Magnetic Fields

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