Chapter 20, Problem 49RPP

BIO Power lines—do their magnetic fields pose a risk? Power lines produce both electric and magnetic fields The interior of the human body is an electrical conductor, and as a result, electric fields are greatly reduced in magnitude within the body The electric fields inside the body from power lines are much smaller than electric fields normally existing in the body.

However, magnetic fields are not reduced in the body Earth's magnetic field, approximately $5\times {10}^{-5}$

T, is very small and not regarded as a health threat Thus, it is interesting to compare Earth's magnetic field to fields produced by high power lines The magnetic field B produced at a distance r from a straight wire with an electric current l is

$B=\left(2\times {10}^{-7}\text{ T }\cdot \text{m/A}\right)I/r$

The magnetic field from a high-voltage power line located 40 m above the ground carrying a 100-A current is much smaller than Earth's $\stackrel{\to }{B}$ field

Wires that provide electric power for household appliances also produce electric and magnetic fields The current in the wire for a 500-W space heater is about 5 A. With the wire located several meters from your body the magnetic field of such an appliance is somewhat smaller than Earth s magnetic field By comparison laboratory mice lived for several generations in 0.0010-T magnetic fields (20 times Earth s magnetic field) without any adverse effects

During the last three decades, electric power use has increased the magnitudes of the $\stackrel{\to }{B}$ field created by power lines to which Americans are exposed by roughly a factor of 20 Yet during that same time interval, leukemia rates have slowly declined It seems unlikely that magnetic fields produced by home appliances or high-voltage power lines are a hazard for causing leukemia

Using your answer to Problem 20.48, determine the quantity closest to the amount that the auxiliary magnetic field causes the magnetic field to vary over a 0.20-m region of the body being mapped by MRI.

a. 4 T

b. 2T

c. 0.002 T

d. 0.02 T

e. 0.2 T