How to solve a Lorentz force problem

[MagnetoBLI]

I am trying to understand how the Lorentz force affects bulk fluid motion when I have an applied electric field (y-axis), applied magnetic field (x-axis) and bulk fluid velocity (z-axis), all orthogonal to each other.

I understand that if the fluid was at rest, an electrostatic force would generate a velocity in the y-axis, which would also generate a Lorentz force/velocity in the z-axis and form the cyclotron effect.

However, when the bulk fluid velocity in the z-axis exists, I presume this flow cannot be considered a moving charge (as both ions and electrons are travelling) and therefore the only moving charge is associated with the electric field. Instead a dynamo effect would take place such that the momentum force of the z-axis fluid flow would generate a current in the negative y-axis (should be negative in the image) and this current would in turn produce a force in the z-axis, thus accelerating the bulk fluid motion. Therefore the net effect would be to increase the radius of the cyclotron affect in the z-axis. Is this correct?

Could you tell me where the magnetic and electric field vectors should be to produce a force perpendicular to the bulk fluid motion (right schematic in the attachment)?

Any comments are much appreciated.

Attachment found in: https://www.physicsforums.com/showthread.php?t=665859

Cheers.

 

[Nate810]

Yes, your understanding is correct. The dynamo effect you mention occurs when the bulk fluid flow (in the z-axis) interacts with the electric field (in the y-axis) to create a current in the negative y-axis, which then produces a force in the z-axis, thus accelerating the bulk fluid motion. This can be thought of as an extension of the cyclotron effect, where the moving charge (in this case the bulk fluid flow) interacts with the magnetic field to produce a force perpendicular to both the electric and magnetic fields. To produce a force perpendicular to the bulk fluid motion, the electric and magnetic field vectors should be arranged such that they form a cross (as shown in the right schematic in the attachment). The electric field should be directed along the y-axis and the magnetic field along the x-axis. This will cause a Lorentz force to be generated along the z-axis, perpendicular to the bulk fluid motion.