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 . Part A Estimate the magnetic field strength on the ground underneath such a line. Express your answer in microtesla. B B = nothing μT SubmitRequest Answer Part B What percentage of the earth’s magnetic field does this represent? (Assume that magnetic field strength at the surface of the earth is 5× 10 −5 T ) Express your answer in percent. B tl B Earth B t l B E a r t h = nothing % SubmitRequest Answer Provide Feedback Next

Answer 1

A) $2.0\cdot 10^{-6} T$

The magnetic field strength around a current-carrying wire is given by the formula

$B=\frac{\mu_0 I}{2\pi r}$

where

$\mu_0 = 1.257 \cdot 10^{-6} H/m$ is the vacuum permeability

I is the current in the wire

r is the radial distance from the wire

In this problem, we have

I = 200 A is the current in the wire

and we want to calculate the magnetic field strength at a distance of

r = 20 m

from the wire, so:

$B=\frac{(1.257\cdot 10^{-6})(200)}{2\pi (20)}=2.0\cdot 10^{-6} T$

B) 4 %

The magnetic field strength at the surface of the Earth is

$B_e = 5\cdot 10^{-5} T$

While the strength of the magnetic field generated by the wire at ground level is

$B=2.0\cdot 10^{-6} T$

Therefore, in percentage, it is:

$\frac{B}{B_e}=\frac{2.0\cdot 10^{-6}}{5\cdot 10^{-5}}\cdot 100 = 0.04 \cdot 100 = 4 \%$