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.1. Estimate the magnetic field strength on the ground underneath such a line.2. What percentage of the earth’s magnetic field does this represent?

Answer 1

A.
`B = 6.36 * 10^(-10) T`

B. P ≈ 0

Step-by-step explanation:

In order to calculate the magnetic field strength we have to use the magnetic field strength of a straight wire.

`B = (mi* I)/(2\pi *d)` (eq. I)

B = magnetic field strength at distance d

I = current (A)

mi = represented by the greek letter μ, represents the permeability of the free space, which is: 4 × π 10^(-7) T m/A

d = distance from the wire

By replacing the values in eq I, we have the following:

`B = (4\pi 10^(-7) T m A^(-1) 200 A)/(2\pi *20 m)\\\\B = 6.36 * 10^(-10) T\\` (eq II)

The earth magnetic field in the surface variates from 25 to 65 microteslas. Thus:

P = Percentage from the wires/percentage of the earth

`P = (6.36 * 10^(-10)T)/(65* 10^(-3) T)\\` ∵
`B << B_(earth)` ∴

P ≈ 0