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https://texercises.com/exercise/magnetic-field-of-a-hydrogen-atom/
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Exercise:
According to the Bohr model of the hydrogen atom the electron orbits the nucleus on a circular trajectory with radius rBO em Bohr radius for ground state. This can be erpreted as a circular current loop. Calculate the corresponding magnetic field.

Solution:
The orbital frequency can be found using the centripetal condition with the electrostatic force acting as the centripetal force: sscFC fracpiepsilon_fracq_p q_er^ frace^piepsilon_ r^ m_e omega^ r pi^ m_e f^ r Solving for the frequency f leads to f sqrtfrace^pi^epsilon_ m_e r^ The current produced by the electron corresponds to I fracDelta QDelta t fraceT e f sqrtfrace^pi^epsilon_ m_e r^ The magnetic field at the centre of the atom is therefore given by B fracmu_ fracIr BF fracncmuotimessqrtfracnce^pi^timesncepstimes metimes rB^ B approx resultBP
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Exercise:
According to the Bohr model of the hydrogen atom the electron orbits the nucleus on a circular trajectory with radius rBO em Bohr radius for ground state. This can be erpreted as a circular current loop. Calculate the corresponding magnetic field.

Solution:
The orbital frequency can be found using the centripetal condition with the electrostatic force acting as the centripetal force: sscFC fracpiepsilon_fracq_p q_er^ frace^piepsilon_ r^ m_e omega^ r pi^ m_e f^ r Solving for the frequency f leads to f sqrtfrace^pi^epsilon_ m_e r^ The current produced by the electron corresponds to I fracDelta QDelta t fraceT e f sqrtfrace^pi^epsilon_ m_e r^ The magnetic field at the centre of the atom is therefore given by B fracmu_ fracIr BF fracncmuotimessqrtfracnce^pi^timesncepstimes metimes rB^ B approx resultBP
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Magnetism
Tags
current, loop, magnetic field, wire
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Difficulty
(4, default)
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Language
ENG (English)
Type
Calculative / Quantity
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