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 11 above the ground. The local power company tells you that the line operates at 16 and provide a maximum of 83 to the local area.

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 11 above the ground. The local power company tells you that the line operates at 16 and provide a maximum of 83 to the local area.

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.]
Express your answer using two significant figures.

Compare to the Earth's field of .
Express your answer using two significant figures.

Answer 1

On AC transmission lines, one line has current going one way, another the opposite direction. Don't the magnetic fields neary add to zero?

Answer 2

To estimate the maximum magnetic field you might experience walking under the power line, we can use the formula for the magnetic field produced by a straight current-carrying wire. The formula is given by:

B = (μ₀ * I) / (2π * r)

Where:
B is the magnetic field in Tesla (T),
μ₀ is the permeability of free space, approximately equal to 4π × 10⁻⁷ T m/A,
I is the current in Amperes (A),
r is the distance from the wire in meters (m).

In this case, the transmission wire is located at a distance of 11 m. The power company tells us that the line operates at 16 A and provides a maximum of 83 kW to the local area.

First, let's convert the maximum power to current:
Power = Voltage × Current
83 kW = 16 V × Current
Current = 83,000 W / 16 V = 5,187.5 A (approximately)

Now, we can plug these values into the formula:
B = (μ₀ * I) / (2π * r)
B = (4π × 10⁻⁷ T m/A * 5,187.5 A) / (2π * 11 m)
B ≈ 7.44 * 10⁻⁴ T

So, the estimated maximum magnetic field you might experience walking under the power line is approximately 7.44 * 10⁻⁴ T.

Now let's compare this to the Earth's magnetic field. The Earth's magnetic field at the surface is typically around 25 to 65 microteslas (µT), with an average value of about 50 µT.

Converting to Tesla, the Earth's magnetic field is 50 × 10⁻⁶ T.

Comparing the two values, we have:
(7.44 * 10⁻⁴ T) / (50 × 10⁻⁶ T) ≈ 0.0149

So, the maximum magnetic field experienced under the power line is approximately 0.0149 times the strength of the Earth's magnetic field.