Deriving the E Cross B Drift Velocity: A Puzzling Explanation

This is not an ansatz, but a fundamental physical principle that can be mathematically derived. In summary, the E cross B drift for a plasma is a fundamental physical principle that can be mathematically derived from the Lorentz force law. The drift velocity is perpendicular to the magnetic field in order for the Lorentz force to be zero. This is not an ansatz, but a unique solution that can be verified by checking the equation preceding (5).
  • #1
pierce15
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I am looking at this brief derivation of the E cross B drift for a plasma, starting at the top of page 3: http://www.physics.sfsu.edu/~lea/courses/grad/motion.PDF.

I am a bit confused as to the justification that the drift velocity is perpendicular to the magnetic field, as stated at the top of page 3. Is this an ansatz, which just happens to work out? One can immediately check that this velocity solves the equation preceding (5), and if I am not mistaken the solution is linear in components of drift velocity so it must be the unique solution.

Or am I missing something and is there a reason why the drift velocity is perpendicular to B?
 
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  • #2
Yes, there is a reason why the drift velocity is perpendicular to B. This is because of the Lorentz force law, which states that the force on a particle in a magnetic field is proportional to the velocity and perpendicular to both the velocity and the magnetic field. Therefore, the drift velocity must be perpendicular to the magnetic field in order for the Lorentz force to be zero.
 

What is the basic concept behind deriving the E Cross B drift velocity?

The E Cross B drift velocity is a phenomenon that occurs in charged particle motion when they are subjected to both electric and magnetic fields. The particles experience a force due to the electric field, and their motion is then deflected in a direction perpendicular to both the electric and magnetic fields.

Why is it considered a puzzling explanation?

The E Cross B drift velocity is often considered a puzzling explanation because it seems counterintuitive that particles would move in a direction perpendicular to both the electric and magnetic fields. It requires a deeper understanding of the underlying physics and the complex interactions between the fields and particles.

How is the E Cross B drift velocity derived?

The E Cross B drift velocity is derived using the Lorentz force equation, which describes the force on a charged particle in an electric and magnetic field. By solving for the velocity of the particle, the E Cross B drift velocity can be calculated.

What factors affect the E Cross B drift velocity?

The E Cross B drift velocity is affected by the strength and direction of the electric and magnetic fields, as well as the charge and mass of the particles. It is also influenced by the velocity of the particles and any collisions or interactions with other particles.

What are some real-world applications of understanding the E Cross B drift velocity?

The E Cross B drift velocity has many important applications in plasma physics, space science, and fusion energy research. It is also crucial for understanding the behavior of particles in particle accelerators and in creating magnetic confinement for nuclear fusion reactions.

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