Exercise
https://texercises.com/exercise/magnetic-field-at-the-center-of-the-cern-accelerator/
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The following quantities appear in the problem: Zeit \(t\) / elektrische Stromstärke \(I\) / elektrische Ladung \(q, Q\) / Magnetische Flussdichte \(B\) / Radius \(r\) / Umfang \(u\) / Anzahl \(N\) /
The following formulas must be used to solve the exercise: \(I = \dfrac{q}{t} \quad \) \(u = 2\pi r \quad \) \(q = N e \quad \) \(B = \dfrac{\mu_0 I}{2r} \quad \)
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Exercise:
At CERN approximately a Neo protons are combined o a particle bunch NzO of which orbit fX times per second in the uO-long circular accelerator before being fired at a target in the experiments. Asing these particles all orbit in the same direction what kind of magnetic field would be expected at the center of the circular accelerator based on the described particle stream?

Solution:
Geg N_ Ne N_ Nz f fO u uO % GesMagnetische FlussdichteB siT % The total charge of all N_ packets with N_ protons each each of which carries an elementary charge e is: al q N_ N_ e Ne Nz nce q. % From the frequency it can be determined after which time all packets have completed a full circular orbit in the accelerator orbit time: al T fracf fracf T. % Somit beträgt die Stromstärke im Beschleuniger: al I fracqT fracN_ N_ efracf N_ N_ ef fracqT I. % Der Radius dieses Kreises beträgt: al r fracupi fracupi r. % Thus the current in the accelerator is: al B fracmu_ Ir fracmu_ N_ N_ efracupi fracpi mu_ ef N_ N_u fracncmuo I r B approx BS % B fracpi mu_ ef N_ N_u BS
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Exercise:
At CERN approximately a Neo protons are combined o a particle bunch NzO of which orbit fX times per second in the uO-long circular accelerator before being fired at a target in the experiments. Asing these particles all orbit in the same direction what kind of magnetic field would be expected at the center of the circular accelerator based on the described particle stream?

Solution:
Geg N_ Ne N_ Nz f fO u uO % GesMagnetische FlussdichteB siT % The total charge of all N_ packets with N_ protons each each of which carries an elementary charge e is: al q N_ N_ e Ne Nz nce q. % From the frequency it can be determined after which time all packets have completed a full circular orbit in the accelerator orbit time: al T fracf fracf T. % Somit beträgt die Stromstärke im Beschleuniger: al I fracqT fracN_ N_ efracf N_ N_ ef fracqT I. % Der Radius dieses Kreises beträgt: al r fracupi fracupi r. % Thus the current in the accelerator is: al B fracmu_ Ir fracmu_ N_ N_ efracupi fracpi mu_ ef N_ N_u fracncmuo I r B approx BS % B fracpi mu_ ef N_ N_u BS
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Attributes & Decorations
Branches
Magnetism
Tags
cern, elektromagnetismus, kreis, kreisstrom, ladung, magnetismus, physik, quelle, stromstärke
Content image
CERN auf Landkarte
Difficulty
(3, default)
Points
3 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator uz
Decoration
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