How Does a Compass React to a Current-Carrying Wire?

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SUMMARY

The discussion focuses on the interaction between a current-carrying wire and a compass, specifically analyzing the magnetic field generated by the wire. The magnetic field due to the wire is calculated using the formula B(wire) = 10^-7(2*I)/r, where 'I' is the current and 'r' is the distance from the wire. The horizontal component of the Earth's magnetic field is approximately 2e-5 tesla, and the net magnetic field (Bnet) is derived from the sum of the Earth's magnetic field and the wire's magnetic field. The calculated magnetic field due to the wire at a distance of 2.9 cm is found to be 3.08532e-7 tesla.

PREREQUISITES
  • Understanding of electromagnetic theory, specifically Ampère's law.
  • Familiarity with magnetic field calculations and vector addition.
  • Knowledge of the formula for the magnetic field around a long straight conductor.
  • Basic proficiency in unit conversions, particularly between centimeters and meters.
NEXT STEPS
  • Calculate the current (I) flowing through the wire using the derived magnetic field values.
  • Explore the effects of varying distances from the wire on the magnetic field strength.
  • Investigate the implications of the compass deflection in relation to the Earth's magnetic field.
  • Learn about the applications of magnetic fields in electrical engineering and physics.
USEFUL FOR

Students studying electromagnetism, physics educators, and anyone interested in the practical applications of magnetic fields in current-carrying conductors.

demonhunter19
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Homework Statement


A long current-carrying wire, oriented North-South, lies on a table (it is connected to batteries which are not shown). A compass lies on top of the wire, with the compass needle about 3 mm above the wire. With the current running, the compass deflects 10 degrees to the West. At this location, the horizontal component of the Earth's magnetic field is about 2e-5 tesla.

What is the magnitude of the magnetic field at location A, on the table top, a distance 2.9 cm to the East of the wire, due only to the current in the wire?


Homework Equations


B(wire)=10^-7(2*I)/r
Bnet = Bearth + Bwire


The Attempt at a Solution


I know Bearth = 2e-5, and taking into account that Bnet would be the deflection, I obtained 2.0308e-5 for Bnet, and hence, Bwire would equal to 3.08532e-7. I don't really know where to go from here.
Thanks in advance.
 
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Well, you've calculated Bwire at r=3mm, so what does that make I? what does that make bwire at r=2.9cm?

Edit- you might also want to show us your calculation of Bnet, because I don't think it is correct.
 

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