Estimate the magnitude of the magnetic field at ground level generated by an overhead AC power line service drop connecting a single home to a utility pole.

Question

Estimate the magnitude of the magnetic field at ground level generated by an overhead AC power line service drop connecting a single home to a utility pole.

Answer 1

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Estimating the magnitude of the magnetic field at ground level generated by an overhead AC power line service drop connecting a single home to a utility pole involves several factors, including the current flowing through the wire, the distance from the wire, and the frequency of the AC power. Let's break down the steps to estimate the magnetic field:

1. **Current in the Wire (I):** Determine the typical current flowing through the power line. In the United States, a common residential service drop might have a current rating of 100 to 200 amperes (A). However, this can vary.

2. **Distance from the Wire (r):** Determine the distance at which you want to estimate the magnetic field. This is typically at ground level, which is approximately 1 to 2 meters (m) from the wire, depending on the height of the wire above the ground.

3. **Frequency (f):** The frequency of the AC power in the United States is typically 60 Hertz (Hz).

4. **Permeability of Free Space (\(μ_0\)):** The permeability of free space, denoted as \(μ_0\), is a constant and is approximately \(4π × 10^{-7}\) tesla meters per ampere (T·m/A). This constant relates magnetic field strength to current and distance.

Now, you can use the formula to estimate the magnetic field (\(B\)) at the given distance from the wire:

\[ B = \frac{{μ_0 \cdot I}}{{2π \cdot r}} \]

- \( B \) is the magnetic field strength (in teslas, T).

- \( μ_0 \) is the permeability of free space (\(4π × 10^{-7}\) T·m/A).

- \( I \) is the current in the wire (in amperes, A).

- \( r \) is the distance from the wire (in meters, m).

Plug in the values:

\[ B = \frac{{(4π × 10^{-7} \, \text{T·m/A}) \cdot I}}{{2π \cdot r}} \]

Simplify:

\[ B = \frac{{2 × 10^{-7} \, \text{T·m/A} \cdot I}}{{r}} \]

Now, let's calculate the magnitude of the magnetic field. Keep in mind that this is a rough estimate and may not take into account all possible factors affecting the magnetic field. Use the values for \(I\) and \(r\) that apply to your specific situation to get an estimate of the magnetic field strength at ground level.