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

Answer:

A. $B = 6.36 * 10^{-10} T$

B. P ≈ 0

Explanation:

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

$B = \frac{mi* I}{2\pi *d}$ (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:

$B = \frac{4\pi 10^{-7} T m A^{-1} 200 A}{2\pi *20 m}\\\\B = 6.36 * 10^{-10} T$ (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

$P = \frac{6.36 * 10^{-10}T}{65* 10^{-3} T}$ ∵ $B << B_{earth}$ ∴

P ≈ 0