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https://texercises.raemilab.ch/exercise/deflecting-a-compass/
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Exercise:
A compass needle is placed in a solenoid which is oriented in east-west direction. The coil is LO long and has NO turns. At a current of IO the compass needle is deflected by thO from its initial direction. Calculate the horizontal component of the earth’s magnetic field.

Solution:
The direction corresponds to the direction of the total magnetic field which consists of the horizontal component of the earth's magnetic field B_H and the field of the solenoid B_S. center includegraphicswidth.mm#image_path:deflecting-compass# center The deflection angle is given by see figure tan theta fracB_SB_H fracmu_ N IL B_H Solving for B_H leads to B_H BHF fracncmuotimes Ntimes ILtimes tanthO BH approx resultBHP-
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Exercise:
A compass needle is placed in a solenoid which is oriented in east-west direction. The coil is LO long and has NO turns. At a current of IO the compass needle is deflected by thO from its initial direction. Calculate the horizontal component of the earth’s magnetic field.

Solution:
The direction corresponds to the direction of the total magnetic field which consists of the horizontal component of the earth's magnetic field B_H and the field of the solenoid B_S. center includegraphicswidth.mm#image_path:deflecting-compass# center The deflection angle is given by see figure tan theta fracB_SB_H fracmu_ N IL B_H Solving for B_H leads to B_H BHF fracncmuotimes Ntimes ILtimes tanthO BH approx resultBHP-
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Attributes & Decorations
Branches
Magnetism
Tags
current, magnetic field, solenoid, superposition
Content image
Difficulty
(2, default)
Points
0 (default)
Language
ENG (English)
Type
Calculative / Quantity
Creator by
Decoration