91Ó°ÊÓ

The radius is$r=6.1\text{m}$

The current is $i=100\text{A}$

Horizontal component of earth’s magnetic field at the site is $20\mathrm{μ}T.$

Consider equation of magnetic field due to current carrying wire at a point away from the wire at a distance r. Using this equation, calculate the magnetic field due to the wire and comparing it with the horizontal component of earth’s magnetic field, we can determine whether it will affect the compass reading or not.

Magnetic field$\left(\mathbf{B}\right)$ due to current$\left(\mathbf{i}\right)$ in the wire at any point at a distance r from the wire is: $\mathbf{B}\mathbf{=}\frac{{\mathbf{μ}}_{\mathbf{0}}\mathbf{i}}{\mathbf{2}\mathbf{Ï€°ù}}$

Here, ${\mathbf{μ}}_{\mathbf{0}}$ is the permeability of the free space.

Magnetic field $\left(B\right)$due to current $\left(i\right)$in the wire at a point and distance r from the wire is:

$B=\frac{{\mathrm{μ}}_{0}i}{2\mathrm{π}r}$

$B=\frac{4\mathrm{π}×{10}^{-7}×100}{2\mathrm{π}×6.1}=3.3×{10}^{-6}T$

$B=3.3\mathrm{μ}T$

Consider the horizontal component of earth’s magnetic field is$20\mathrm{μ}T$.The value we got is approximately one sixth of the magnetic field of earth.

Therefore, it will affect the compass reading.