Have you ever wondered how a force on electrons in a metal plate translates to a force on the plate itself? This is a fascinating question that has puzzled scientists for a long time. In this article, we will take a closer look at how the Lorentz force, which is experienced by the conduction electrons in the metal, produces a force on the plate as a whole.
The Lorentz Force and Conduction Electrons
To understand how a force on electrons in a metal plate can produce a force on the plate as a whole, we first need to understand what the Lorentz force is and how it affects conduction electrons. The Lorentz force is the force experienced by a charged particle, such as an electron, when it moves through a magnetic field. The force perpendicular to both the velocity of the electron and the magnetic field is given by:
F = q(v x B)
where F is the Lorentz force, q is the charge of the electron, v is its velocity, and B is the magnetic field. When an aluminium plate enters an external magnetic field, the Lorentz force is exerted on the conduction electrons in the aluminium plate. The velocity of the plate and the magnetic field are orthogonal to each other, so an induced current moves along a closed path.
Scattering and Confinement
When a force is exerted on the atoms in a solid, it is almost immediately transmitted to the electrons in the solid. Why is this so? The answer lies in the concepts of scattering and confinement. Scattering occurs because electrons are constantly moving around and colliding with atoms. If the electrons and atoms are moving with respect to each other, they will “drag” on each other, which has the effect of tending to bring the velocities into sync. This “drag” is responsible for electrical resistance.
Confinement, on the other hand, means that electrons are stuck in the metal. The electrons are attracted to the nuclei in the metal, and there’s a significant force, quantified by the work function, keeping them in the metal. If the electrons and atoms are moving with respect to each other, the electrons will pile up at one end and empty out at the other end, creating a force counteracting this pile-up. The effect is to bring the velocities of the electrons and atoms into sync.
How Does the Force Get Transmitted to the Plate?
Now that we have a better understanding of the Lorentz force and scattering and confinement, we can start to answer the question of how a force on electrons gets transmitted to the aluminium plate as a whole. When a nonferromagnetic conductor passes between the poles of a magnet, an electric field is induced, and circulating currents called eddy currents are generated. As a result, a magnetic damping force is induced on the eddy currents, which opposes the motion of the conductor.
A horizontal magnetic force is exerted on the portion of the eddy current that is within the magnetic field. This force is transmitted to the aluminium plate and is the retarding force associated with the magnetic braking. The scattering and confinement of the conduction electrons ensure that the force is transmitted to the plate as a whole, rather than just affecting individual electrons.
Why Doesn’t the Force Get Transferred Orthogonally to the Direction of Motion?
One question that may arise is why the Lorentz force, which is due to the motion of the aluminium plate with respect to the magnetic field, is not transferred to the plate as a whole, resulting in a force orthogonal to the direction of motion on the whole plate. The reason is that the scattering and confinement of the electrons cause them to move in sync with the atoms in the plate. As a result, the net force on the plate due to the Lorentz force will be in the direction of motion.
Conclusion
The transmission of a force on electrons to a metal plate as a whole is a fascinating topic that involves concepts such as the Lorentz force, scattering, and confinement. We have seen how the scattering and confinement of conduction electrons ensure that a force on them is transmitted to the plate as a whole, and why the force is not transferred orthogonally to the direction of motion.
By understanding these concepts, we can gain a greater appreciation for the fundamental processes that occur within materials and how they respond to external stimuli.
How Does a Force On Electrons Produce a Force On a Metal Plate
Have you ever wondered how a force on electrons in a metal plate translates to a force on the plate itself? This is a fascinating question that has puzzled scientists for a long time. In this article, we will take a closer look at how the Lorentz force, which is experienced by the conduction electrons in the metal, produces a force on the plate as a whole.
The Lorentz Force and Conduction Electrons
To understand how a force on electrons in a metal plate can produce a force on the plate as a whole, we first need to understand what the Lorentz force is and how it affects conduction electrons. The Lorentz force is the force experienced by a charged particle, such as an electron, when it moves through a magnetic field. The force perpendicular to both the velocity of the electron and the magnetic field is given by:
where F is the Lorentz force, q is the charge of the electron, v is its velocity, and B is the magnetic field. When an aluminium plate enters an external magnetic field, the Lorentz force is exerted on the conduction electrons in the aluminium plate. The velocity of the plate and the magnetic field are orthogonal to each other, so an induced current moves along a closed path.
Scattering and Confinement
When a force is exerted on the atoms in a solid, it is almost immediately transmitted to the electrons in the solid. Why is this so? The answer lies in the concepts of scattering and confinement. Scattering occurs because electrons are constantly moving around and colliding with atoms. If the electrons and atoms are moving with respect to each other, they will “drag” on each other, which has the effect of tending to bring the velocities into sync. This “drag” is responsible for electrical resistance.
Confinement, on the other hand, means that electrons are stuck in the metal. The electrons are attracted to the nuclei in the metal, and there’s a significant force, quantified by the work function, keeping them in the metal. If the electrons and atoms are moving with respect to each other, the electrons will pile up at one end and empty out at the other end, creating a force counteracting this pile-up. The effect is to bring the velocities of the electrons and atoms into sync.
How Does the Force Get Transmitted to the Plate?
Now that we have a better understanding of the Lorentz force and scattering and confinement, we can start to answer the question of how a force on electrons gets transmitted to the aluminium plate as a whole. When a nonferromagnetic conductor passes between the poles of a magnet, an electric field is induced, and circulating currents called eddy currents are generated. As a result, a magnetic damping force is induced on the eddy currents, which opposes the motion of the conductor.
A horizontal magnetic force is exerted on the portion of the eddy current that is within the magnetic field. This force is transmitted to the aluminium plate and is the retarding force associated with the magnetic braking. The scattering and confinement of the conduction electrons ensure that the force is transmitted to the plate as a whole, rather than just affecting individual electrons.
Why Doesn’t the Force Get Transferred Orthogonally to the Direction of Motion?
One question that may arise is why the Lorentz force, which is due to the motion of the aluminium plate with respect to the magnetic field, is not transferred to the plate as a whole, resulting in a force orthogonal to the direction of motion on the whole plate. The reason is that the scattering and confinement of the electrons cause them to move in sync with the atoms in the plate. As a result, the net force on the plate due to the Lorentz force will be in the direction of motion.
Conclusion
The transmission of a force on electrons to a metal plate as a whole is a fascinating topic that involves concepts such as the Lorentz force, scattering, and confinement. We have seen how the scattering and confinement of conduction electrons ensure that a force on them is transmitted to the plate as a whole, and why the force is not transferred orthogonally to the direction of motion.
By understanding these concepts, we can gain a greater appreciation for the fundamental processes that occur within materials and how they respond to external stimuli.