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 $$I_rms$$.
$$V_{rms}=\frac{V_0}{\sqrt{2}}\\$$

$$V_{rms} = \frac{10kV}{\sqrt{2}}$$

$$V_{rms} = 7071.07V$$

$${and}$$

$$P = V_{rms}*I_{rms}$$

$$40E6 = 7071.07 * I_{rms}$$

$$I_{rms} = 5656.85A$$


ANd i have no ideas what should i go next
I don't really get what does the change of the direction of the magnetic field have to do with the magnitude. Isnt that would be the same no matter what?

The attached image is what I am thinking right now
[edit] i will upload the image later, because i need to fix my scanner [/edit]

 

[learningphysics]

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'm a little concerned with how the question is phrased. The way I read it Vrms=10kV. Pmax=40MW

Vmax=10*sqrt(2) kV=14142KW

Imax=Pmax/Vmax=2828A

You need maximum current to get maximum magnetic field.

Anyway, I think you're right about the location of the maximum magnetic field. You're only looking for the maximum so the fact that it is changing doesn't matter.

Get the magnetic field due to one wire(assume it is an infinite wire). Sketch the vector on your diagram. Get the magnitude field due to the second wire. Sketch the vector. Do the vector addition, and get the magnitude of the sum.

 

[thepatientmental]

first

Based on the information provided, we can estimate the maximum magnetic field experienced under the power lines using the formula B = (μ0 * I)/(2π * r), where μ0 is the permeability of free space, I is the current, and r is the distance from the wire.

Using the values given, we can calculate the current as 5656.85 amps and the distance from the wire as 1.5m (half of the 3m distance between the wires). The permeability of free space is a constant value of 4π * 10^-7 T*m/A. Plugging in these values, we get:

B = (4π * 10^-7 T*m/A * 5656.85 A)/(2π * 1.5m)

B = 0.000094 T

This means that the maximum magnetic field experienced under the power lines is 0.000094 Tesla, which is significantly lower than the Earth's magnetic field of approximately 0.00005 Tesla.

It's important to note that this is an estimate and the actual magnetic field may vary depending on factors such as the exact distance from the wire, the current fluctuations, and the direction of the magnetic field. However, it is unlikely that the magnetic field under the power lines would be significantly higher than the Earth's field.

As for the change in direction of the magnetic field, it does affect the magnitude as it is a vector quantity. However, for the purpose of this estimation, we can assume that the average magnitude of the field is what is being measured.

I hope this helps clarify the situation. If you have any further questions, please let me know.