Cosmic Rays passing through a magnetic field

In summary, to calculate the cyclotron radius and time for one orbit of a relativistic particle in a magnetic field, you need to use the Lorentz force, relativistic momentum, and Newton's Second Law to set up equations of motion. You also need to know the velocity, magnetic field strength, and Lorentz factor of the particle. The angle of 45 degrees and equal components of momentum are important in determining the velocity in the x and y directions, and ultimately the total velocity of the particle.
  • #1
Gogsey
160
0
Assume that it hits the Galactic magnetic field at an angle of 45o, i.e. such that
the components of its momentum parallel and perpendicular to the magnetic field
are equal. What is its cyclotron radius? How long does it take to execute one
cyclotron orbit?

W ealso, know velocity From part a0. which I didn't post), magnetic field strength, and the Lorentz factor, since were accounting for relativistic objects?

Mainly I'm not sure about the whole 45 degrre angle and equal components of momentum and how they relate to cyclotron motion.
 
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  • #2
You need to set up your equations of motion. Start with the Lorentz force on the electron, making sure to use the relativistic momentum.
 
  • #3
Ok, so we have:

P(x)=gamma*mV(x)cos 45
P(y)=gamma*mV(y)sin 45

So this means the velocity in the y and x directions are not equal, but the momentums are.

Therefore we are left with V(x)cos 45 = V(y)sin 45.

Now which velocity are we interested in? Is it the combined velocity? Do we have to write one in terms of the other, and then solve for this value, then use this to find the other and find the total velocity? How do we do this using only one equation?
 
  • #4
You did not write the components of momentum correctly. Write it down as a vector before trying to decompose it into components.

To calculate a trajectory, you first need to set up an equation of motion. In this case, you will need Newton's Second Law ([tex]\vec{F}[/tex] = d[tex]\vec{p}[/tex]/dt). The relativistic momentum is [tex]\vec{p}[/tex] = [tex]\gamma[/tex]m[tex]\vec{v}[/tex]. The vector force is q[tex]\vec{v}[/tex]x[tex]\vec{B}[/tex].
 

Related to Cosmic Rays passing through a magnetic field

1. What are cosmic rays?

Cosmic rays are highly energetic particles, mainly protons and atomic nuclei, that originate from sources outside of the Earth's atmosphere. They can have energies millions of times higher than those produced by particle accelerators on Earth.

2. How are cosmic rays affected by a magnetic field?

Cosmic rays are charged particles, so they are affected by magnetic fields. When they pass through a magnetic field, they experience a force called the Lorentz force, which can cause them to change direction and spiral around the field lines.

3. What causes cosmic rays to spiral through a magnetic field?

The Lorentz force, which is a result of the interaction between the charged cosmic rays and the magnetic field, causes them to spiral along the field lines. This is similar to the way charged particles spiral in a particle accelerator.

4. How do cosmic rays interact with the Earth's magnetic field?

The Earth's magnetic field acts as a shield, deflecting and trapping most of the cosmic rays coming from space. However, some cosmic rays with very high energies can penetrate the magnetic field and reach the Earth's surface.

5. Can cosmic rays passing through a magnetic field cause any harm?

In general, cosmic rays passing through a magnetic field do not pose a threat to humans. However, astronauts and airline crew members who are exposed to high levels of cosmic rays on a regular basis may face an increased risk of developing certain health issues, such as cataracts and cancer.

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