Final answer:
To calculate the magnetic and electric energy densities at the surface of a 3.0-mm-diameter copper wire carrying an 18-A current, we would use Ampère's Law for magnetic field and include calculations for resistance to find the electric field, in order to determine the corresponding energy densities using formulas that involve the permeability and permittivity of free space.
Step-by-step explanation:
The question is asking to calculate the magnetic and electric energy densities at the surface of a 3.0-mm-diameter copper wire carrying an 18-A current, considering the resistance of the wire.
To find the magnetic energy density, we must first calculate the magnetic field (B) around the wire using Ampère's Law. Since the wire's exact pattern of current distribution isn't provided, a precise calculation isn't possible. However, the general formula for magnetic energy density (μ) at a point in space is given by μ = B^2/(2µ), where µ is the permeability of free space.
For the electric energy density (ε), we would need to determine the electric field (E) in the wire based on the resistance and the current flowing through it. The electric energy density can be calculated using the formula ε = ½ε_0E^2, where ε_0 is the permittivity of free space.
To include resistance in these calculations, we may also use Ohm's Law (V = IR) and the resistivity formula for a cylindrical object (R = ρL/A), where ρ is the resistivity of copper, L is the length of the wire, and A is the cross-sectional area.