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Exercise:
Two long straight aluminium Formelbuch.grampercubiccentimeter wires each of diameter .mm carry the same current -- but in opposite directions. They are susped by .m long strings. If the suspension strings make an angle of ang. with the vertical what is the current in the wires?

Solution:
newqtyrA.ekgpcm newqtyd.m newqtyL.m newqtya.degree newqtymuo.newtonpersquareampere % The vertical component of the string force must compensate the weight of the wire. Thus its horizontal component must compensate the Biot-Savart force acting on the wire. Considering the right wire we can write solqtyIsqrtfracpi^rho d^ g L sinalphatanalphamu_sqrtpi***rAn*dn***ncgn*Ln*sindan*tandan/muonA F_leftarrow &mustbe F_rightarrow sscFBS fracFGcosalpha sinalpha Iell B mg tanalpha Iell fracmu_ Ipi R rho V g tanalpha Iell fracmu_ Ipi L sinalpha rho pi r^ ell g tanalpha fracmu_ I^pi L sinalpha rho pi r^ g tanalpha I sqrt fracpi^ rhomu_ r^ g L sinalpha tanalpha If sqrtfracpi^ rA qtyd^ ncg L sina tanamuo I III
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Exercise:
Two long straight aluminium Formelbuch.grampercubiccentimeter wires each of diameter .mm carry the same current -- but in opposite directions. They are susped by .m long strings. If the suspension strings make an angle of ang. with the vertical what is the current in the wires?

Solution:
newqtyrA.ekgpcm newqtyd.m newqtyL.m newqtya.degree newqtymuo.newtonpersquareampere % The vertical component of the string force must compensate the weight of the wire. Thus its horizontal component must compensate the Biot-Savart force acting on the wire. Considering the right wire we can write solqtyIsqrtfracpi^rho d^ g L sinalphatanalphamu_sqrtpi***rAn*dn***ncgn*Ln*sindan*tandan/muonA F_leftarrow &mustbe F_rightarrow sscFBS fracFGcosalpha sinalpha Iell B mg tanalpha Iell fracmu_ Ipi R rho V g tanalpha Iell fracmu_ Ipi L sinalpha rho pi r^ ell g tanalpha fracmu_ I^pi L sinalpha rho pi r^ g tanalpha I sqrt fracpi^ rhomu_ r^ g L sinalpha tanalpha If sqrtfracpi^ rA qtyd^ ncg L sina tanamuo I III
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Branches
Magnetism
Tags
electromagnetism, force, fore, lorentz, lorentzforce, magnetic, magnetism, physics, trigonometry, vector, wire
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Difficulty
(4, default)
Points
3 (default)
Language
ENG (English)
Type
Calculative / Quantity
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Link