Exercise
https://texercises.com/exercise/solar-wind-particles-captured-in-van-allen-belt/
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The following quantities appear in the problem: Masse \(m\) / elektrische Ladung \(q, Q\) / Magnetische Flussdichte \(B\) / Kraft \(F\) / Geschwindigkeit \(v\) / Radius \(r\) /
The following formulas must be used to solve the exercise: \(F = qvB \quad \) \(F = m\dfrac{v^2}{r} \quad \)
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Exercise:
An proton coming from the Sun enters the Earth's magnetic field high above the equator where its strength is BaO at a speed of vO. This place is located about km to km above the Earth's surface and is called the Van Allen Belt. The proton then moves in an almost circular path -- apart from a slight northward drift -- along the magnetic field lines. There near the North Pole the strength of the magnetic field is BnO. Calculate the radius of the protons's orbit over both the equator and the North Pole.

Solution:
Geg textProtonpf m ncmp sscBA  BaO Ba v v sscBN  BnO Bn % GesRadiusrsim % The Lorentz force acting on the protons forces them to go around the magnetic field lines in a circle. Setting this force equal to the force required for anything making a circle we get: sscFL sscFZ qvB mfracv^r r fracmvqB For a proton with charge qe we get in the magnetic field above the equator sscrA fracmvqsscBA fracncmp vnce Ba ra approx raP and at the North Pole sscrN fracmvqsscBN fracncmp vnce Bn rn approx rnP. r fracmvqsscBA sscrA raP sscrN rnP
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Exercise:
An proton coming from the Sun enters the Earth's magnetic field high above the equator where its strength is BaO at a speed of vO. This place is located about km to km above the Earth's surface and is called the Van Allen Belt. The proton then moves in an almost circular path -- apart from a slight northward drift -- along the magnetic field lines. There near the North Pole the strength of the magnetic field is BnO. Calculate the radius of the protons's orbit over both the equator and the North Pole.

Solution:
Geg textProtonpf m ncmp sscBA  BaO Ba v v sscBN  BnO Bn % GesRadiusrsim % The Lorentz force acting on the protons forces them to go around the magnetic field lines in a circle. Setting this force equal to the force required for anything making a circle we get: sscFL sscFZ qvB mfracv^r r fracmvqB For a proton with charge qe we get in the magnetic field above the equator sscrA fracmvqsscBA fracncmp vnce Ba ra approx raP and at the North Pole sscrN fracmvqsscBN fracncmp vnce Bn rn approx rnP. r fracmvqsscBA sscrA raP sscrN rnP
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Tags
elektromagnetismus, kreisbahn, lorentzkraft, magnetfeld, physik
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(2, default)
Points
2 (default)
Language
ENG (English)
Type
Calculative / Quantity
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