You want to get an idea of the magnitude of magnetic fields produced by overhead

Question

You want to get an idea of the magnitude of magnetic fields produced by overhead power lines. You estimate that a transmission wire is about 13 m above the ground. The local power company tells you that the line operates at 13 kV and provide a maximum of 64 MW to the local area.

a. Estimate the maximum magnetic field you might experience walking under such a power line, and compare to the Earth's field. [For an ac current, values are rms, and the magnetic field will be changing.]

b. Compare to the Earth's field of 5.0×105T.

Explanation / Answer

a)

Power = Voltage*Current

or P = Vrms*Irms

So, Irms = P/Vrms = 64*10^6/(13*10^3) = 4923.1 A

So, maximum magnetic field due to the wire = u*Io/(2*pi*r)

Now, Io = Irms*sqrt(2)

= 1.26*10^-6*(4293.1*sqrt(2))/(2*pi*13)

= 9.37*10^-5 T <-----answer

b)

So, the magnetic field is (9.37*10^-5)/(5*10^-5) = 1.87 times the Earth's Magnetic field

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