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