Transmission Lines and Health. Currents in dc transmission lines can be 100 A or higher. Some people are concerned that the electromagnetic fields from such lines near their homes could pose health dangers. For a line that has current 170 A and a height of 8.0 m above the ground, what magnetic field does the line produce at ground level? Express your answer in teslas and as a percentage of the earth's magnetic field, which is 0.50 G. Is this value cause for worry?

Calculate the magnetic field strength at the ground. Treat the transmission line as infinitely long. The magnetic field strength is then given by:

B = μ₀I / (2πr)

B = magnetic field strength, μ₀ = magnetic constant, I = current, r = distance from line

Given values:

μ₀ = 4π*10⁻⁷H/m, I = 170A, r = 8.0m

Plug in and solve for B:

B = 4π*10⁻⁷ (170) / (2π (8.0))

B = 4.25*10⁻⁶T

The earth's magnetic field strength is 0.50G or 5.0*10⁻⁵T. Calculate the ratio of the line's magnetic field strength to earth's magnetic field strength:

4.25*10⁻⁶ / (5.0*10⁻⁵)

= 0.085

= 8.5%

The transmission line's magnetic field strength is 8.5% of that of earth's natural magnetic field. This is no cause for worry.