How Does the Hall Effect Influence a Suspended Metal Bar in a Magnetic Field?

[KFC]

Homework Statement

There is a metal bar was suspended by a spring between the ceiling and its top. Apply an electric field, from left right. Find out what happen with the bar after applying and magnetic field perpendicular to the electric filed and point out of page.


2. The attempt at a solution
When we apply the magnetic field, negative charge start to be moved from the bottom to the top due to the hall effect. In this stage, the bar will suffer extra Lorentz force downward, so the spring will suffer a downward force also. After some time, when more and more negative charge being moved to the top of the bar, an uniform electric field was established and pointing from bottom to the top to balance out the Lorentz force so the spring restore back it the equilibrium position. I am wondering if my analysis is correct or not?

 

[Jhero]

Your analysis is partially correct. When the magnetic field is applied, the electrons in the metal bar will experience a sideways force due to the Lorentz force. This will cause them to accumulate on one side of the bar, creating a separation of charge. However, instead of an electric field being established from bottom to top, it will be established from left to right, perpendicular to the direction of the magnetic field. This is known as the Hall effect.

As the charge accumulates on one side of the bar, it will create an electric field that opposes the magnetic field. This will result in a net force on the bar in the opposite direction of the magnetic field, causing it to move in the direction of the electric field. This motion will continue until the charges reach a steady state distribution, at which point the bar will stop moving.

So, in summary, your analysis is correct in that the bar will experience a Lorentz force and the spring will be affected, but the direction of the electric field will be perpendicular to the magnetic field and will cause the bar to move in the opposite direction.