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

Answer 1

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