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https://texercises.com/exercise/compact-muon-solenoid/
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Exercise:
The em Compact Muon Solenoid CMS is one of the large detectors at the em Large Hadron Collider LHC at CERN. It contains a solenoid with a length of lO and a radius of rO. The strength of the magnetic field in the solenoid is BO for a current of IO. abcliste abc Calculate the energy stored in the magnetic field. abc Calculate the inductance of the solenoid. abcliste

Solution:
abcliste abc The magnetic energy density is w_m fracB^mu_ The energy stored in the magnetic field is W_m w_m ell r^pi WmF labelenergy fracB^timesncmuotimes ltimes r^timespi Wm approx resultWmP As a comparison: The kinetic energy of an Airbus A airliner is about gigaJ. abc The energy stored in the magnetic field can also be written as: W_m fracL I^ Setting this equal to refenergy and solving for the inductance leads to L LF fracB^times ltimes r^times pincmuotimes I^ L approx resultLP abcliste
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Exercise:
The em Compact Muon Solenoid CMS is one of the large detectors at the em Large Hadron Collider LHC at CERN. It contains a solenoid with a length of lO and a radius of rO. The strength of the magnetic field in the solenoid is BO for a current of IO. abcliste abc Calculate the energy stored in the magnetic field. abc Calculate the inductance of the solenoid. abcliste

Solution:
abcliste abc The magnetic energy density is w_m fracB^mu_ The energy stored in the magnetic field is W_m w_m ell r^pi WmF labelenergy fracB^timesncmuotimes ltimes r^timespi Wm approx resultWmP As a comparison: The kinetic energy of an Airbus A airliner is about gigaJ. abc The energy stored in the magnetic field can also be written as: W_m fracL I^ Setting this equal to refenergy and solving for the inductance leads to L LF fracB^times ltimes r^times pincmuotimes I^ L approx resultLP abcliste
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Branches
Magnetism
Tags
electromagnetic induction, inductance, magnetic energy
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Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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Decoration
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