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Exercise:
You would like to let a piece of copper wire LO long dO diameter float in a uniform magnetic field with strength BO. Sketch a possible orientation of magnetic field and current with directions and calculate the required magnitude of the current. Is the idea realistic?

Solution:
For a horizontal wire with a current flowing from left to right the downward gravitational force F_G has to be compensated by an upright magnetic force F_B. Using the right-hand rule we find that the magnetic field has to po o the drawing plane. includegraphicswidth.textwidth#image_path:floating-wire# Asing the direction of the magnetic field is perpicular to the wire the force equlibrium F_BF_G can be expressed as I L B m g sscrhoCu V g mF g Here the volume of the wire is expressed as the volume of a cylinder with length L and radius d/: V L r^ pi L leftfracdright^ pi Solving for the current leads to I fracsscrhoCu L d^pi g L B IF fracRKutimesd^timespitimesncgtimesB I approx resultIP The result is realistic but there is no easy way to connect the wire to a current supply without adding extra weight.
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Exercise:
You would like to let a piece of copper wire LO long dO diameter float in a uniform magnetic field with strength BO. Sketch a possible orientation of magnetic field and current with directions and calculate the required magnitude of the current. Is the idea realistic?

Solution:
For a horizontal wire with a current flowing from left to right the downward gravitational force F_G has to be compensated by an upright magnetic force F_B. Using the right-hand rule we find that the magnetic field has to po o the drawing plane. includegraphicswidth.textwidth#image_path:floating-wire# Asing the direction of the magnetic field is perpicular to the wire the force equlibrium F_BF_G can be expressed as I L B m g sscrhoCu V g mF g Here the volume of the wire is expressed as the volume of a cylinder with length L and radius d/: V L r^ pi L leftfracdright^ pi Solving for the current leads to I fracsscrhoCu L d^pi g L B IF fracRKutimesd^timespitimesncgtimesB I approx resultIP The result is realistic but there is no easy way to connect the wire to a current supply without adding extra weight.
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Attributes & Decorations
Branches
Magnetism
Tags
biot-savart, magnetic force
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Decoration
Content image