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https://texercises.com/exercise/compass-next-to-cable/
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The following quantities appear in the problem: elektrische Stromstärke \(I\) / Magnetische Flussdichte \(B\) / Winkel \(\theta\) /
The following formulas must be used to solve the exercise: \(B = \dfrac{\mu_0 I}{2\pi r} \quad \) \(\tan\alpha = \dfrac{a}{b} \quad \)
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Exercise:
A compass is placed rO south of a cable carrying a current IO from top to bottom. Calculate the angle by which the compass needle is deflected if the horizontal component of the Earth's magnetic field at this po is BeO.

Solution:
center tikzpicture nodecolorOrange at bigotimes; nodecolorOrange at . I; drawcolorblue dashed circle cm; drawgreen - latex -.----. nodeleft midway r; drawultra thick red - stealth ----.; drawultra thick green -.---; tikzpicture center Geg r rO r I I sscBE BeO Be GesAnglealphasirad At a distance of rO the strength of the conductor magnetic field is al sscBL fracmu_ Ipi r fracncmu Ipi r  Bl. At the location of the compass needle the Earth's magnetic field sscBE acts from geographically south to north and the conductor magnetic field sscBL acts from east to west. The two magnetic fields form the opposite sides of a right-angled triangle. The angle is therefore al alpha arctanfracsscBLsscBE arctanfracfracmu_ Ipi rsscBE arctanfracmu_Ipi r sscBE fracBlBe adP arS arP towards the west. % a arctanfracmu_Ipi r sscBE adP arS arP
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Exercise:
A compass is placed rO south of a cable carrying a current IO from top to bottom. Calculate the angle by which the compass needle is deflected if the horizontal component of the Earth's magnetic field at this po is BeO.

Solution:
center tikzpicture nodecolorOrange at bigotimes; nodecolorOrange at . I; drawcolorblue dashed circle cm; drawgreen - latex -.----. nodeleft midway r; drawultra thick red - stealth ----.; drawultra thick green -.---; tikzpicture center Geg r rO r I I sscBE BeO Be GesAnglealphasirad At a distance of rO the strength of the conductor magnetic field is al sscBL fracmu_ Ipi r fracncmu Ipi r  Bl. At the location of the compass needle the Earth's magnetic field sscBE acts from geographically south to north and the conductor magnetic field sscBL acts from east to west. The two magnetic fields form the opposite sides of a right-angled triangle. The angle is therefore al alpha arctanfracsscBLsscBE arctanfracfracmu_ Ipi rsscBE arctanfracmu_Ipi r sscBE fracBlBe adP arS arP towards the west. % a arctanfracmu_Ipi r sscBE adP arS arP
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Tags
eines, elektromagnetismus, erdmagnetfeld, leiter, magnetfeld, physik, vektor, vektoraddition, winkel
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Difficulty
(2, default)
Points
2 (default)
Language
ENG (English)
Type
Calculative / Quantity
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Link