Charged Particle Moving in a Magnetic Field

In summary, the conversation discusses the relationship between speed, radius, and period of a charged particle in a magnetic field. It is mentioned that if the speed of the particle increases, the radius of its circular trajectory also increases, while the time remains constant. There is a discrepancy between this and the inverse relationship between velocity and period, which is explained through the concept of the "initial path." The conversation also mentions the use of gyrofrequency to calculate the period in this scenario.
  • #1
Farina
39
0
Hello. Can you please check out the attachment?

Solving (a) is easy. The correct answer to (b) is "the period for the return trip is unchanged" (that is, T = 130 ns).

Okay, fine: the attachment shows why T only depends on m, q, and B.

How on Earth, though, do you reconcile this with the inverse relationship between velocity and period, given the initial and return arc radius values are the same?

In other words, if KE is doubled, the speed increases, and (again for a constant radius) the period must DECREASE!

What am I missing? Thank you!
 

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  • #2
If the speed of a charged particle in a magnetic field increases, the radius of the circular trajectory also increases. If the speed doubles the radius and so the circumference of the circle doubles and the time remains constant.
 
  • #3
Thank you!

And, right, that's the rub... the problem statement (taken from Halliday & Resnick) specified:

"If the particle is sent back though the magnetic field (along the same initial path)..."

My guess this "same initial path" specification is incorrect.

HallsofIvy said:
If the speed of a charged particle in a magnetic field increases, the radius of the circular trajectory also increases. If the speed doubles the radius and so the circumference of the circle doubles and the time remains constant.
 
  • #4
Why is that? The same initial path is the downward arrow on the right. It goes that way once, then again with twice the energy.
 
  • #5
Twice the energy means 1.4 times the speed, which means a 1.4 times greater radius for a given period, T.
 
  • #6
Ok, is there a problem with that? I have not checked your numbers, but assume that you did it fine. Note that the path through the magnetic field is not the initial path. Is that what is tripping you up?
 
  • #7
The stated problem text said: "... along the same initial path" which I take to mean the initial path and return path are one and the same?

ModusPwnd said:
Ok, is there a problem with that? I have not checked your numbers, but assume that you did it fine. Note that the path through the magnetic field is not the initial path. Is that what is tripping you up?
 
  • #8
lol, why would you take it like that? Initial path means initial path, the path the on the right. Initial doesn't mean initial and return...
 
  • #9
It is better learning to work it out as you have, but you could also get the answer from the equation for the gyrofrequency (or cyclotron frequency).
from
https://en.wikipedia.org/wiki/Cyclotron_resonance
https://en.wikipedia.org/wiki/Gyroradius

The gyrofrequency is the (angular) frequency for full revolution, but your problem is half a circle, so you should be able to see that it is just double the frequency. And you can take the inverse to get period. It doesn't depend on velocity at all since the velocity cancels out (in the nonrelativistic regime).
 

Related to Charged Particle Moving in a Magnetic Field

What is a charged particle moving in a magnetic field?

A charged particle moving in a magnetic field is a fundamental concept in physics that describes the behavior of charged particles, such as electrons or protons, when they are subjected to a magnetic field. This phenomenon is known as the Lorentz force and is responsible for the motion of charged particles in many natural and man-made systems.

How does a charged particle move in a magnetic field?

A charged particle moving in a magnetic field experiences a force perpendicular to both its velocity and the magnetic field. This force causes the particle to follow a curved path, known as a helix, around the direction of the magnetic field. The direction of the force is determined by the right-hand rule, with the thumb pointing in the direction of the particle's velocity and the fingers pointing in the direction of the magnetic field.

What factors affect the motion of a charged particle in a magnetic field?

The motion of a charged particle in a magnetic field is affected by several factors, including the strength of the magnetic field, the charge and mass of the particle, and the velocity of the particle. A stronger magnetic field will result in a tighter helical path, while a greater charge or mass will result in a stronger force on the particle. The direction of the particle's velocity also plays a role, as a perpendicular velocity will result in a circular path, while a parallel velocity will result in no deflection.

What are some real-world applications of charged particles moving in a magnetic field?

The concept of charged particles moving in a magnetic field has many practical applications, including particle accelerators, mass spectrometers, and magnetic resonance imaging (MRI) machines. It is also used in everyday devices such as electric motors and generators, which rely on the interaction between a magnetic field and charged particles to produce motion or electricity.

How is the motion of a charged particle in a magnetic field related to electricity?

The behavior of charged particles in a magnetic field is closely related to electricity, as both are fundamental forces in physics. The motion of charged particles in a magnetic field can be used to generate electricity, and the reverse is also true, with electricity being used to create a magnetic field. This relationship is described by Maxwell's equations, which unify the fields of electricity and magnetism into the single concept of electromagnetism.

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