- #1
Adeonaja
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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?
Trajectory of charged particles in a magnetic field?
- Thread starter Adeonaja
- Start date
In summary, Griffiths explains that when a charge enters a magnetic field perpendicularly, its motion will be circular. However, since it is accelerated, it will also radiate energy and its motion should be a spiral inward. This loss of energy is known as synchrotron radiation, as confirmed by a Google search. Without an exact citation, it is likely that Griffiths is considering a situation where the energy loss and deviation from the ideal trajectory are small enough to be ignored. Interested readers can refer to Griffiths's chapter on radiation or Problem 11.16 in the 3rd edition for more information.
- #2
Nugatory
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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
jtbell
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Or look in Griffiths's chapter on radiation near the end of the book.Nugatory said:
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.
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 due to the interaction between the magnetic field and the particle's electric charge. The particle will experience a force perpendicular to both its velocity and the direction of the magnetic field, causing it to move in a circular or helical path.
How does the strength of the magnetic field affect the trajectory of a charged particle?
The strength of the magnetic field directly affects the radius of the charged particle's trajectory. A stronger magnetic field will result in a smaller radius, while a weaker magnetic field will result in a larger radius. This is because the force on the charged particle is directly proportional to the strength of the magnetic field.
What is the role of the particle's velocity in its trajectory in a magnetic field?
The particle's velocity plays a crucial role in its trajectory in a magnetic field. The direction of the velocity determines the direction of the force on the particle, while the magnitude of the velocity determines the strength of the force. A higher velocity will result in a larger radius of the trajectory, while a lower velocity will result in a smaller radius.
Can the trajectory of a charged particle in a magnetic field be controlled?
Yes, the trajectory of a charged particle in a magnetic field can be controlled by changing the strength or direction of the magnetic field, or by changing the velocity of the particle. This is the principle behind devices such as particle accelerators and mass spectrometers.
How is the trajectory of a charged particle affected by the charge and mass of the particle?
The charge and mass of the particle do not affect the trajectory itself, but they do affect the strength of the force on the particle. A particle with a higher charge or lower mass will experience a stronger force, resulting in a smaller radius of the trajectory. Conversely, a particle with a lower charge or higher mass will experience a weaker force, resulting in a larger radius.
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