Questions: Although the evidence is weak, there has been concern in recent years over possible health effects from the magnetic fields generated by electric transmission lines. A typical high-voltage transmission line is 20 m above the ground and carries a 200 A current at a potential of 110 kV. Part A What is the magnetic field strength on the ground directly under such a transmission line? Express your answer with the appropriate units. B= Value Units

Solution Steps

The magnetic field \( B \) generated by a long straight current-carrying wire at a distance \( r \) from the wire is given by the formula: \[ B = \frac{\mu_0 I}{2 \pi r} \] where:

• \( \mu_0 \) is the permeability of free space (\( \mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A} \)),
• \( I \) is the current in the wire,
• \( r \) is the distance from the wire.

Given:

• \( I = 200 \, \text{A} \),
• \( r = 20 \, \text{m} \).

Substitute these values into the formula: \[ B = \frac{(4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}) \times 200 \, \text{A}}{2 \pi \times 20 \, \text{m}} \]

Simplify the expression by canceling out common terms: \[ B = \frac{4 \times 10^{-7} \times 200}{2 \times 20} \] \[ B = \frac{8 \times 10^{-5}}{40} \] \[ B = 2 \times 10^{-6} \, \text{T} \]

Final Answer