# Magnetic Bottle and the Kinetic Energy of a Charged Particle

• fog37
In summary: This is not what I was expecting.In summary, when a charged particle is inside a magnetic bottle at the right speed, the particle bounces back and forth and is confined inside the magnetic field. The magnetic force does not work on the particle hence the particle's kinetic energy remains constant. The particle may change direction at the end of the bottles but will never stop (zero KE).
fog37
Hello,

When a charged particle is inside a magnetic bottle at the right speed, the particle bounces back and forth and is confined inside the magnetic field.
The magnetic force does not work on the particle hence the particle's kinetic energy remains constant.

That means that the particle may change direction at the end of the bottles but will never stop (zero KE), correct? What happens is that the longitudinal speed goes to zero but not the transverse speed keeping KE constant. Essentially, the particle does not stop but simply turns out without stopping...

Is that correct?

Thanks!

That is correct.

fog37
Does it not lose some energy because the charged particle's acceleration generates some EM radiation?

berkeman said:
Does it not lose some energy because the charged particle's acceleration generates some EM radiation?
Sure, northern lights but on a much smaller scale.

berkeman
kuruman said:
That is correct.
Thank you. I have read some author mention that the charged particle STOPs (zero KE) before changing direction...I guess that is an incorrect oversimplification. Also, my question implies that only the magnetic force ##F_B## is present (NO electric field ##E##). However, there is a nonzero longitudinal magnetic field gradient in the magnetic bottle due to the nonuniform ##B## field.
• The force acting on the particles seems to be ##F = B \times \nabla B## instead of simply ##F = qv \times B##
• From the charged particle perspective (frame of reference), the B field is changing in time, which causes an electric field, in virtue of Maxwell's equation. The generated ##E## field produces an electric force on the particle that slows it down...

fog37 said:
I have read some author mention that the charged particle STOPs (zero KE) before changing direction...I guess that is an incorrect oversimplification
You know the rules...

fog37
kuruman said:
Sure, northern lights but on a much smaller scale.
Actually, the optical emission we see as the northern lights is not due to radiation from accelerating charged particles. Instead, what is happening is that the precipitating particles collide with neutral atoms and molecules (mostly atomic oxygen and molecular nitrogen). Those collisions either bump those neutrals into higher energy states or ionize them. When the oxygen and nitrogen go back down to lower energy states they emit the light that we see as the aurora.

jason

zoki85, vanhees71 and berkeman
jasonRF said:
Actually, the optical emission we see as the northern lights is not due to radiation from accelerating charged particles. Instead, what is happening is that the precipitating particles collide with neutral atoms and molecules (mostly atomic oxygen and molecular nitrogen). Those collisions either bump those neutrals into higher energy states or ionize them. When the oxygen and nitrogen go back down to lower energy states they emit the light that we see as the aurora.

jason
I stand corrected.

vanhees71
berkeman said:
You know the rules...

Thank you berkeman, I was reading physics notes on various websites and none seem to indicate that when the charged particle is "reflected", the KE does not change so the particle keeps the same speed while it does the turnaround at the magnetic bottle's edge and does not really slow down or stop.

## 1. What is a magnetic bottle?

A magnetic bottle is a device that uses magnetic fields to trap charged particles, such as ions or electrons, within a confined region. The particles are confined by the magnetic field lines, which form a loop or bottle shape, hence the name "magnetic bottle".

## 2. How does a magnetic bottle work?

A magnetic bottle works by using a combination of electric and magnetic fields to create a region of high magnetic field strength. This strong magnetic field traps the charged particles, preventing them from escaping. The particles are then confined within the bottle and can be manipulated or studied by adjusting the strength and orientation of the magnetic fields.

## 3. What is the kinetic energy of a charged particle in a magnetic bottle?

The kinetic energy of a charged particle in a magnetic bottle is the energy associated with its motion within the bottle. This energy is determined by the strength of the magnetic field and the mass and charge of the particle. As the particle moves within the bottle, its kinetic energy may change due to interactions with the magnetic field and other particles.

## 4. How is the kinetic energy of a charged particle related to its motion in a magnetic bottle?

The kinetic energy of a charged particle is directly related to its motion in a magnetic bottle. As the particle moves within the bottle, it experiences a force from the magnetic field, causing it to accelerate. The kinetic energy of the particle increases as it gains speed and decreases as it slows down. The exact relationship between kinetic energy and motion in a magnetic bottle can be described by the equations of motion for a charged particle in a magnetic field.

## 5. What are some practical applications of magnetic bottles and the kinetic energy of charged particles?

Magnetic bottles and the kinetic energy of charged particles have many practical applications in fields such as particle physics, plasma physics, and fusion energy research. They are also used in medical imaging technologies such as magnetic resonance imaging (MRI), which uses magnetic bottles to trap and manipulate particles in the body to create detailed images. Additionally, magnetic bottles are used in particle accelerators to manipulate and control the motion of particles for experiments and research.

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