# Predicting Lorentz force fluid particle trajectories

• MagnetoBLI
In summary, when an electric and magnetic field are applied orthogonal to each other and to the bulk fluid motion, the Lorentz force will cause a current to be induced, resulting in an acceleration of the fluid flow in the z-axis. This can be seen through the cyclotron effect and the dynamo effect, ultimately increasing the radius of the cyclotron effect in the z-axis.
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.

Cheers.

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Yes, your understanding is correct. The Lorentz force will cause a current to be induced in the direction of the electric field vector, which in turn will create a force perpendicular to both the electric and magnetic field vectors. This force will result in an acceleration of the bulk fluid flow in the z-axis. The magnetic and electric field vectors should be pointing in opposite directions (as shown in the right schematic in the attachment) in order to produce this perpendicular force.

## 1. What is the Lorentz force?

The Lorentz force is a fundamental concept in physics that describes the force exerted on a charged particle moving through an electromagnetic field. It is a combination of the electric force, which is exerted by the electric field, and the magnetic force, which is exerted by the magnetic field.

## 2. How is the Lorentz force used in predicting fluid particle trajectories?

In fluid dynamics, the Lorentz force is used to predict the trajectory of a charged fluid particle in an electromagnetic field. This is important for understanding phenomena such as plasma flow, ionized gas dynamics, and magnetohydrodynamics.

## 3. What factors affect the trajectory of a fluid particle in an electromagnetic field?

The trajectory of a fluid particle is affected by several factors, including the strength and direction of the electric and magnetic fields, the charge and mass of the particle, and the initial velocity of the particle. The shape and size of the particle can also play a role in its trajectory.

## 4. How can the Lorentz force be calculated and predicted?

The Lorentz force can be calculated using the equations of motion for a charged particle in an electromagnetic field. These equations take into account the electric and magnetic fields, as well as the velocity and charge of the particle. With these calculations, the trajectory of the particle can be predicted.

## 5. What are some real-world applications of predicting Lorentz force fluid particle trajectories?

Some real-world applications of predicting Lorentz force fluid particle trajectories include understanding the behavior of plasma in fusion reactors, modeling the motion of charged particles in Earth's magnetosphere, and designing electromagnetic propulsion systems for spacecraft. It is also used in various industrial processes, such as controlling the flow of conductive fluids in metallurgy and metal casting.

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