Final answer:
To calculate the current in the wire needed to create a 5.00 × 10^-5 T field at a distance of 100 m from a long straight 200-kV DC power line, we can use the formula B = μ₀I/2πr. By rearranging the formula and substituting the given values, we can find the current required.
Step-by-step explanation:
A surveyor 100 m from a long straight 200-kV DC power line suspects that its magnetic field may equal that of the Earth and affect compass readings. To calculate the current in the wire needed to create a 5.00 × 10-5 T field at this distance, we can use the formula B = μ₀I/2πr, where B is the magnetic field, μ₀ is the permeability of free space, I is the current, and r is the distance from the wire. Rearranging the formula, we have I = (2πrB)/μ₀. Substituting the given values, we get I = (2π * 100 * 5.00 × 10-5)/ (4π × 10-7). Solving this equation gives us the current required.