Name: charged particle paths in magnetic fields
Uploaded: 2023-04-30T12:40:48.000Z
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Motion Of A Charged Particle In A Magnetic Field

Considérons une masse ponctuelle m de charge Q se déplaçant perpendiculairement à un champ magnétique uniforme B.
L'intensité de la force de Lorentz est constante et est toujours perpendiculaire à sa vitesse. Ainsi, il ne peut pas changer l'intensité de la vitesse, mais seulement sa direction. Par conséquent, la trajectoire de la particule est un cercle de rayon r.
En utilisant la deuxième loi du mouvement de Newton, la force de Lorentz est égale à la force centripète. Ainsi, le rayon du cercle est calculé.
La période de temps T de la trajectoire circulaire de la particule est la circonférence par la vitesse. En substituant la valeur de r, on obtient T.
Si la vitesse n’est pas perpendiculaire au champ magnétique, le composant parallèle au champ magnétique n’est pas affecté, produisant ainsi un mouvement constant le long du champ magnétique. Par conséquent, la particule se déplace sur une trajectoire hélicoïdale.
Dans la formule du rayon, la composante perpendiculaire de la vitesse est substituée. Comme T est indépendant de la vitesse, il reste le même.
Son pas est défini comme la distance entre les virages adjacents, donnée par le produit de la composante parallèle de la vitesse et de la période.

<ol>
	<li>OpenStax. (2019). Physique universitaire Vol. 2. [Version Web], section 11.3, pages 501 à 506. Récupéré de <a href="https://openstax.org/books/university-physics-volume-2/pages/11-3-motion-of-a-charged-particle-in-a-magnetic-field">Mouvement d’une particule chargée dans un champ magnétique</a></li>
</ol>

mouvement d'une particule chargée dans un champ magnétique

Une particule chargée subit une force lorsqu'elle se déplace dans un champ magnétique. Considérez le champ comme étant uniforme et la particule chargée se déplaçant perpendiculairement à celui-ci. Si le champ est dans le vide, le champ magnétique est le facteur déterminant du mouvement. Étant donné que la force magnétique est perpendiculaire à la direction du mouvement, une particule chargée suit une trajectoire courbée. La particule continue à suivre cette trajectoire courbée jusqu'à former un cercle complet. Une autre façon de voir cela est que la force magnétique est toujours perpendiculaire à la vélocité, de sorte qu'elle ne travaille pas sur la particule chargée. L'énergie cinétique et la vitesse de la particule restent ainsi constantes. La force affecte la direction du mouvement mais pas la vitesse. Par conséquent, la particule se déplace en cercle. Le temps que met la particule chargée pour faire le tour de la trajectoire circulaire est défini comme la période, qui est la même que la distance parcourue pour faire un cycle complet, ou la circonférence du cercle divisée par la vitesse.

Si la vélocité n'est pas perpendiculaire au champ magnétique, alors chaque composante de la vélocité doit être comparée séparément au champ magnétique. La composante de la vélocité perpendiculaire au champ magnétique produit une force magnétique perpendiculaire à la fois à cette vélocité et au champ. La composante parallèle au champ magnétique crée un mouvement constant dans la même direction que le champ magnétique. Le mouvement parallèle détermine le pas de l'hélice, qui est défini comme la distance entre les tours adjacents. Il est égal à la composante parallèle de la vélocité multipliée par la période. Le résultat est un mouvement hélicoïdal.

Pendant que la particule chargée se déplace sur une trajectoire hélicoïdale, elle peut entrer dans une région où le champ magnétique n'est pas uniforme. En particulier, supposons qu'une particule se déplace d'une région de fort champ magnétique vers une région de champ plus faible, puis revienne vers une région de champ plus fort. La particule peut revenir en arrière avant d'entrer dans la région de champ magnétique plus fort. Cela ressemble à une onde sur une corde se déplaçant d'une corde très légère et fine à un mur solide et réfléchissant en arrière. Si la réflexion se produit aux deux extrémités, la particule est piégée dans une soi-disant bouteille magnétique.

Mouvement d'une particule chargée dans un champ magnétique

Une particule chargée subit une force lorsqu’elle se déplace dans un champ magnétique. Considérons que le champ est uniforme et que la particule chargée se déplace ...

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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

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Charged Particle Paths in Magnetic Fields | JoVE K12

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Charged Particle Paths in Magnetic Fields

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