A surveyor is using a magnetic compass 6.1 m below a power line in which there is a steady curre

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A surveyor is using a magnetic compass 6.1 m below a power...

A surveyor is using a magnetic compass 6.1 $\mathrm{m}$ below a power line in which there is a steady current of 100 A. (a) What is the magnetic field at the site of the compass due to the power line? (b) Will this field interfere seriously with the compass reading? The horizontal component of Earth's magnetic field at the site is 20$\mu \mathrm{T}$ .

A surveyor is using a magnetic compass 6.1 $\mathrm{m}$ below a power line
in which there is a steady current of
100 A. (a) What is the magnetic
field at the site of the compass due
to the power line? (b) Will this field interfere seriously with the compass reading? The horizontal component of Earth's magnetic field at
the site is 20$\mu \mathrm{T}$ .

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Key Concepts

Magnetic Field of a Long Straight Conductor

This concept involves calculating the magnetic field generated by a current-carrying conductor using the formula B = ??I/(2?r). It is derived from Ampère’s law or the Biot–Savart law and is fundamental in understanding how currents produce magnetic fields that diminish with distance from the source.

Earth's Magnetic Field

Earth's magnetic field, which typically has a horizontal component of tens of microteslas, is the field responsible for the behavior of compass needles. Its magnitude and direction are essential for navigation and play a crucial role when additional magnetic fields are present, as they can interfere with compass readings.

Superposition of Magnetic Fields

This principle states that the net magnetic field at any point is the vector sum of the individual magnetic fields present. When considering the magnetic field produced by a nearby current-carrying conductor and Earth’s magnetic field, their contributions add up vectorially, which is important in determining the overall effect on instruments like a compass.

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