Question

Although the evidence is weak, there has been concern in recent years over possible health effects from the magnetic fields generated by electric transmission lines. A typical high-voltage transmission line is $20\mathrm{m}$above the ground and carries a $200\mathrm{A}$current at a potential of $110\mathrm{kV}$.

a. What is the magnetic field strength on the ground directly under such a transmission line?

b. What percentage is this of the earth’s magnetic field of $50\mathrm{\mu T}$?

Short answer

(a) The magnetic field strength is $2\mathrm{\mu T}.$

(b) Percentage will be$4\%.$

Step-by-step solution

Part (a) Step 1: Given information

We have given,

Height of transmission line =$20\mathrm{m}$

Current ion transmission line =$200\mathrm{A}$

we have to find the magnetic field at the ground due to transmission line.

Simplify

The magnetic field strength due to long wire is

$$\begin{gathered} \mathrm{B}=\frac{{\mathrm{\mu }}_0\mathrm{I}}{2\mathrm{\pi R}}=\frac{4\mathrm{\pi }\times {10}^{-7}\times 200}{2\mathrm{\pi }\times 20} \\ \mathrm{B}=2\times {10}^{-6}\mathrm{T} \end{gathered}$$

Part (b) Step 1: Given information

We have given,

Magnetic field of the earth = $50\times {10}^{-6}\mathrm{T}$

we have to find the percentage of transmission magnetic strength to earth magnetic strength.

Simply

The percentage will be

$$\begin{gathered} \mathrm{percentage}=\frac{\mathrm{magnetic}\mathrm{field}\mathrm{of}\mathrm{wire}}{\mathrm{magnetic}\mathrm{field}\mathrm{of}\mathrm{earth}}\times 100\% \\ \mathrm{percentage}=\frac{2}{5}\times 100\% \\ \mathrm{percentage}=4\% \end{gathered}$$