Question regarding to magnetic field

[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 $$I_rms$$.
$$V_{rms}=\frac{V_0}{\sqrt{2}}\\\ \\V_{rms} = \frac{10kV}{\sqrt{2}}\\ \\V_{rms} = 7071.07V \\ \\\mbox{and}\\ P = V_{rms}*I_{rms}\\ 40E6 = 7071.07 * I_{rms}\\ I_{rms} = 5656.85A$$

 

[Andrew Mason]

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 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

 

[thepatientmental]

To estimate the maximum magnetic field, we can use the formula B = μ0*I/2πr, where μ0 is the permeability of free space, I is the current, and r is the distance from the wire. In this case, we can assume that the current is the maximum value of 5656.85A and the distance from the wire is 1.5m (half of the distance between the wires). Plugging these values into the formula, we get a maximum magnetic field of approximately 1.26 x 10^-4 Tesla.

To compare this to the Earth's magnetic field, we can use the fact that the Earth's magnetic field at the surface is approximately 0.00005 Tesla. This means that the maximum magnetic field from the power lines is about 2,500 times stronger than the Earth's magnetic field. This may seem like a significant difference, but it's important to note that the Earth's field is relatively weak and can vary greatly depending on location and other factors. Additionally, the magnetic field from the power lines will decrease with distance, so it will likely not have a significant effect on someone walking under the lines. However, it's always important to exercise caution when near high voltage power lines and follow any safety precautions provided by the power company.