# Question regarding to magnetic field

1. Mar 15, 2005

### leolaw

You want to get an idea of the magnitude of magnetic fields produced by overhead power lines, You estimate that the two wires are each about 30m above the ground and are about 3m apart. The local power company tells you that the lines operate at 10kV and provide a maximum of 40MW to the local area. Estimate the maximum magnetic field you might experience walking under these power lines, and compare to the Earth's field. (For an ac current, values are rms, and the magnetic field will be changing)

I don't quite understand the problem but i believe that the maximum magnetic field is below and between the two wires. I also found the $$V_rms$$ and $$I_rms$$.
$$V_{rms}=\frac{V_0}{\sqrt{2}}\\\ \\V_{rms} = \frac{10kV}{\sqrt{2}}\\ \\V_{rms} = 7071.07V \\ \\\mbox{and}\\ P = V_{rms}*I_{rms}\\ 40E6 = 7071.07 * I_{rms}\\ I_{rms} = 5656.85A$$

2. Mar 16, 2005

### Andrew Mason

I think they expect you to use Ampere's law and take the field B of a wire carrying a current (using Irms instead of peak) at maximum power of 40 Megawatts. I don't think that the two wires separated by 3 m makes much difference to the final result but you could take each wire separately and add them together.

$$\int B \cdot ds = \mu_0I$$

$$B = \frac{\mu_0I}{2\pi D}$$

where I = the current at 10 Kv and 20 MW (P=VI) in each wire.
and D = 30 m.

The magnetic field of the earth is about 4.5 e-5 Tesla.

AM