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Exercise:
A horizontal wire is hung from the ceiling of a room by two light strings. The wire as a length of LO and a mass of mO. A uniform magnetic field of magnitude BO is directed from the ceiling to the floor. When a current of IO flows through the wire the wire swings upward. In its equilibrium position it makes an angle phi with respect to the vertical. abcliste abc Calculate the angle phi. abc Calculate the tension in the string. abcliste

Solution:
abcliste abc There are three forces acting on the wire: the gravitational force F_G vertical the magnetic force F_B horizontal and the tension force F_T acting along the wire. The force equilibrium can be separated o the vertical and horizontal direction. For the vertical direction the equilibrium is given by F_G F_Tcosphi Solving this for the tension leads to F_T fracF_Gcosphi labeltension For the horizontal direction the equilibrium is given by F_B F_T sinphi Using reftension we find F_B fracF_Gcosphi sinphi F_G tanphi It follows for the angle phi phi arctanfracF_BF_G phiradF arctanfracItimes Ltimes Bmtimes ncg phirad approx resultphidegP abc The tension is given by reftension: F_T fracF_Gcosphi FTF fracmtimes ncgcosphideg FT approx resultFTP abcliste
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Exercise:
A horizontal wire is hung from the ceiling of a room by two light strings. The wire as a length of LO and a mass of mO. A uniform magnetic field of magnitude BO is directed from the ceiling to the floor. When a current of IO flows through the wire the wire swings upward. In its equilibrium position it makes an angle phi with respect to the vertical. abcliste abc Calculate the angle phi. abc Calculate the tension in the string. abcliste

Solution:
abcliste abc There are three forces acting on the wire: the gravitational force F_G vertical the magnetic force F_B horizontal and the tension force F_T acting along the wire. The force equilibrium can be separated o the vertical and horizontal direction. For the vertical direction the equilibrium is given by F_G F_Tcosphi Solving this for the tension leads to F_T fracF_Gcosphi labeltension For the horizontal direction the equilibrium is given by F_B F_T sinphi Using reftension we find F_B fracF_Gcosphi sinphi F_G tanphi It follows for the angle phi phi arctanfracF_BF_G phiradF arctanfracItimes Ltimes Bmtimes ncg phirad approx resultphidegP abc The tension is given by reftension: F_T fracF_Gcosphi FTF fracmtimes ncgcosphideg FT approx resultFTP abcliste
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Attributes & Decorations
Branches
Magnetism
Tags
biot-savart, force equilibrium, magnetic force, tension
Content image
Difficulty
(3, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
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Decoration
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