Question

Currents in dc transmission lines can be 100 A or higher. Some people areconcerned that the electromagnetic fields from such lines near their homes could pose health dangers. For a line that has current 150A and a height of 8 m above the ground, what magnetic field does the line produce at ground level? Express your answer in tesla and as a percentage of the earth’s magnetic field, which is 05 G . Is this value cause for worry?

Short answer

The magnetic field of earth has a magnitude of about$B=5\times {10}^{-5}T$ , so the field produced by the transmission line is 7.5 % of the Earth’s magnetic field.

Step-by-step solution

The formula to be used in the problem

We need to find the magnetic field at the ground due to a transmission line that has current of$I=150A$ at a height of$r=8m$ above the ground. We will treat the line as a very long and straight wire.

The magnetic field due to a very long wire is given by$\mathit{B}\mathbf{=}\frac{{\mathbf{\mu }}_{\mathbf{0}}\mathbf{I}}{\mathbf{2}\mathbf{\pi r}}$ .

Find the magnetic field using the formula

$\begin{array}{r}B=\frac{{\mu }_{0}I}{2\pi r}\\ B=\frac{2\times {10}^{-7}\times 150}{8}\\ B=3.8\times {10}^{-6}\mathrm{T}\end{array}$

The magnetic field of earth has a magnitude of about$B=5\times {10}^{-5}T$ , so the field produced by the transmission line is 7.5 % of the Earth’s magnetic field.