Question

A surveyor is using a magnetic compass $6.1\,m$ below a power line in which there is steady current of $100A$.
(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 $20\mu T$.

Answer 1

Hint:In order to answer this question, to find the magnetic field at the site of the compass due to the power line, as we have the given radius or distance and the current, so we will apply the formula of Magnetic field.

Complete step by step answer:
(a) A magnetic field is a vector field that explains the magnetic influence on moving electric charges, electric currents, and magnetic materials. A moving charge in a magnetic field experiences a force perpendicular to its own velocity and to the magnetic field. The magnitude of the magnetic field due to the current in the wire, at a point a distance $r$ from the wire, is given by-
$B = \dfrac{{{\mu _0}i}}{{2\pi r}}$
where, $B$ is the magnetic field.
$r = 20\,ft = 6.10\,m$
so, we have:
$B = \dfrac{{(4\pi \times {{10}^{ - 7}}T.m/A)(100A)}}{{2\pi (6.10m)}} \\
\Rightarrow B = 3.3 \times {10^{ - 6}}T \\
\therefore B = 33\,\mu T$
Hence, the required magnetic field is $33\,\mu T$ at the site of the compass due to the power line.

(b) This is about one-sixth the magnitude of the Earth’s field. It will affect the compass reading.

Note:- The magnetic field, also known as the B field, is the area where a magnet's power exists. There are two ways to depict the magnetic field: vector field and magnetic field lines. The magnetic field is mathematically described as a vector field. The magnetic field is thought to have both magnitude and direction.