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 11m above the ground. The local power company tells you that the line operates at 13kV and provide a maximum of 57MW 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

Explanation / Answer

A)

Volatage of the line, V = 13 kV = 13*10^4 V

Power , P = 57 MW = 57*10^6 W

distance from the ground , d = 11 m

We know,

Magnetic field due to a current carrying wire at a distance d from the wire is give by :

B = uI/(2*pi*d)

where u = 1.26*10^-6

I = current in the wire

pi = 3.14

We also know,

Power, P = V*I

So, I = P/V = 57*10^6/(13*10^3) = 4384.6 A

So, B = 1.26*10^-6*(4384.6)/(2*3.14*11) = 8*10^-5 T <------answer

B)

So, it is about = (8/5) = 1.6 times than the Earth's field <--------answer

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