Surveyor is using a magnetic compass 8.3 m below a power line in which there is a steady current of 120 A. (a) What is the magnetic field in microteslas 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 µT.

Given Information:  

Current in power line = I = 120 A

distance from power line = r = 8.3 m

Required Information:  

Magnetic field in (µT) at the site of the compass = B = ?

Magnetic field in at the site of the compass = 2.89 µT

Step-by-step explanation:  

(a) What is the magnetic field in µT at the site of the compass due to the power line?

A current carrying power line produces a magnetic field given by Biot-Savart Law,

B = μ₀I/2πr

Where μ₀ is the permeability of free space, I is the current flowing through power line and r is the distance between the power line and magnetic compass.

B = (4πx10⁻⁷*120)/(2π*8.3)

B = 2.89 µT

Therefore, a magnetic field of 2.89 µT will be produced 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 µT.

This magnetic field produced due to the power line will interfere with the compass reading.

tan⁻¹(2.89/20) = 8.22°

Which means that compass reading will be deviated from its true value by 8.22° when magnetic field due to the power line and the Earth’s magnetic field are perpendicular with respect to each other.

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