At what distance from the central axis of a long straight thin wire carrying a current of 5.0 A is the magnitude of the magnetic field due to the wire equal to the strength of the Earth's magnetic field of about 5.0 * 10-5 T?

The magnetic field at a given distance from a very long (essentially infinitely long) current-carrying wire is given by:

B = μ₀I / (2πr)

B = magnetic field strength, μ₀ = magnetic constant, I = current, r = distance from wire

Given values:

B = 5.0*10⁻⁵T, μ₀ = 4π*10⁻⁷H/m, I = 5.0A

Plug in and solve for r:

5.0*10⁻⁵ = 4π*10⁻⁷ (5.0) / (2πr)

r = 0.02m