30.10
Fem en mouvement
Le flux magnétique dépend de trois facteurs : la force du champ magnétique, la zone à travers laquelle les lignes de champ passent, et l'orientation d…
Considérons qu’une tige conductrice de longueur L se déplace avec une vitesse v constante dans le champ magnétique B qui pointe dans le plan de l’écran.
La force magnétique agissant sur une charge positive à l’intérieur d’une tige conductrice est vers le haut, ce qui entraîne l’accumulation de charges opposées aux deux extrémités de la barre. Cela crée un champ électrique, dans le sens descendant.
Les charges continuent de s’accumuler jusqu’à ce que la force électrique soit suffisamment grande pour équilibrer la force magnétique. La différence de potentiel aux bornes de la tige est présente tant qu’elle se déplace.
Si cette tige forme une boucle conductrice fermée avec un conducteur stationnaire en forme de U, les charges libres de la tige se redistribuent le long de la boucle. Cela génère un courant en boucle fermée, et la tige mobile génère une force électromotrice de mouvement connue sous le nom de f.é.m. de mouvement.
Ici, le flux magnétique passant par la boucle fermée est égal au champ magnétique multiplié par l’aire de la boucle. Selon la loi de Faraday, le taux de variation du flux magnétique est égal à l'amplitude de la f.é.m. en mouvement.
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Q1: What causes a motional emf to develop in a moving conducting rod?
When a conducting rod moves through a magnetic field, the magnetic force acts on positive charges within the rod, pushing them toward one end. This charge accumulation creates an electric field that opposes further charge movement. The potential difference that develops across the rod persists as long as the rod continues moving, generating a motional emf.
Q2: How does a closed conducting loop generate current from a moving rod?
When a moving rod forms a closed conducting loop with a stationary U-shaped conductor, free charges redistribute throughout the loop. This redistribution of charges generates a current in the closed loop. The moving rod acts as a source of motional emf that drives this current flow through the complete circuit.
Q3: What is the relationship between magnetic flux change and motional emf?
According to Faraday's law, the magnitude of motional emf equals the rate of change of magnetic flux through the loop. As the conducting rod moves, the area of the loop changes, altering the magnetic flux passing through it. This changing flux directly determines the induced emf in the system.
Q4: What three factors determine the magnetic flux in a motional emf system?
Magnetic flux depends on the strength of the magnetic field, the area through which field lines pass, and the field's orientation relative to the surface. In motional emf systems, the area changes as the rod moves, causing flux variation. Any change in these three factors produces a corresponding change in magnetic flux.
Q5: How does energy conservation apply to motional emf in a conducting loop?
In motional emf systems, the power delivered by the rod's motion must equal the power dissipated by the induced current. This energy conservation principle ensures that mechanical work done moving the rod is converted into electrical energy and then into heat through resistance in the circuit.
Q6: How does a rail gun use motional emf principles to propel projectiles?
A rail gun replaces the conducting rod with a projectile and uses controlled magnetic field changes to decrease flux between the rails. This flux decrease causes current to flow through the armature holding the projectile. The current-carrying armature experiences a magnetic force that propels the projectile forward.
Q7: Why do opposite charges accumulate at the ends of a moving conducting rod?
The magnetic force on positive charges within the moving rod pushes them toward one end, leaving negative charges at the other end. This charge separation continues until the resulting electric field creates an electric force strong enough to balance the magnetic force, establishing equilibrium.