Question

Although the evidence is weak, there has been concern in recent years over possible health effects from the magnetic fields generated by transmission lines. A typical high-voltage transmission line is 20 m off the ground and carries a current of 200 A.

Estimate the magnetic field strength on the ground underneath such a line.

What percentage of the earth’s magnetic field does this represent?

Answer 1

Concepts and reason

The concept used is magnetic field at the surface.

Initially form the expression of the magnetic field, it depends on the distance from the surface and the current flowing through it.

Use the value of magnetic field to calculate the percentage of the earth’s magnetic field.

Fundamentals

The expression of the magnetic field is expresses as follows,

$B = \frac{{{\mu _0}I}}{{2\pi R}}$

Here, ${\mu _0}$ is the permittivity of the free space, $I$ is the current and $R$ is the distance from the point.

Calculate the magnetic field.

The expression of the magnetic field is as follows:

$B = \frac{{{\mu _0}I}}{{2\pi R}}$

Substitute $4\pi \times {10^{ - 7}}{\rm{ H/m}}$ for ${\mu _0}$ , $200{\rm{ A}}$ for $I$ and $20{\rm{ m}}$ for $R$ in the above expression of the magnetic field.

$\begin{array}{c}\\B = \frac{{\left( {4\pi \times {{10}^{ - 7}}{\rm{ H/m}}} \right)\left( {200{\rm{ A}}} \right)}}{{\left( {2\pi } \right)\left( {20{\rm{ m}}} \right)}}\\\\ = 2 \times {10^{ - 6}}{\rm{ T}}\\\end{array}$

The approximate magnetic field at it the surface of the earth is,

${B_1} = 50 \times {10^{ - 6}}{\rm{ T}}$

The expression for the percentage magnetic field with respect to the earth magnetic field is expresses as follows:

$\% {\rm{ of B of earth field = }}\frac{B}{{{B_1}}} \times 100$

Substitute $2 \times {10^{ - 6}}{\rm{ T}}$ for $B$ and $50 \times {10^{ - 6}}{\rm{ T}}$ for ${B_1}$ in the above expression of the percentage,

$\begin{array}{c}\\\% {\rm{ of B of earth field = }}\frac{{2 \times {{10}^{ - 6}}{\rm{ T}}}}{{50 \times {{10}^{ - 6}}{\rm{ T}}}} \times 100\\\\ = 4\% \\\end{array}$

Ans:

The magnetic field strength is equal to $2 \times {10^{ - 6}}{\rm{ T}}$ .

The percentage of the earth magnetic field is equal to $4\%$ .