Trajectory of charged particles in a magnetic field?

  • #1
3
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A charge is entering magnetic field perpendicularly! Griffiths says it motion will be circular! But it is accelerated so it must radiate energy and it's motion should be spiral inward?
 
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  • #2
Google for "synchrotron radiation"; it does indeed lose energy. Without an exact citation we can't be sure, but chances are that Griffith is considering a situation in which the energy loss to radiation and deviation from the zero-energy-loss trajectory are small enough to ignore.
 
  • #3
Nugatory said:
Google for "synchrotron radiation"
Or look in Griffiths's chapter on radiation near the end of the book. :oldwink:

In my copy of the 3rd edition, he considers synchrotron radiation in Problem 11.16 on page 465, which asks the student to derive the power loss when ##\vec v## and ##\vec a## are perpendicular.
 

1. What is the trajectory of a charged particle in a magnetic field?

The trajectory of a charged particle in a magnetic field is a curved path, known as a helix, due to the interaction between the magnetic field and the particle's electric charge.

2. How does the strength of the magnetic field affect the trajectory of a charged particle?

The strength of the magnetic field affects the radius of the helix, with a stronger magnetic field resulting in a smaller radius and a weaker magnetic field resulting in a larger radius.

3. What is the role of the particle's velocity in its trajectory in a magnetic field?

The particle's velocity determines the pitch (spacing) of the helix, with a higher velocity resulting in a smaller pitch and a lower velocity resulting in a larger pitch.

4. How does the charge of the particle affect its trajectory in a magnetic field?

The charge of the particle determines the direction of the helix, with a positively charged particle following a helix in one direction and a negatively charged particle following a helix in the opposite direction.

5. What is the equation for calculating the trajectory of a charged particle in a magnetic field?

The equation for calculating the trajectory of a charged particle in a magnetic field is given by: r = (mv sinθ) / (qB), where r is the radius of the helix, m is the mass of the particle, v is its velocity, θ is the angle between the velocity and the magnetic field, q is the charge of the particle, and B is the strength of the magnetic field.

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