- What is the proximity effect?
- Nearby conductors carrying AC create magnetic fields that distort each other's current distribution. Current crowds toward or away from neighboring conductors, increasing AC resistance beyond skin effect alone.
- Why does Rac/Rdc rise with frequency?
- As frequency increases, skin depth shrinks. The same current uses a thinner effective region near the surface, and nearby conductors further crowd the current, so the effective resistance rises.
- Why does the skin effect increase the effective resistance of a wire at high frequencies?
- The skin effect confines current to a thinner cross-sectional area near the surface. Since resistance is inversely proportional to the effective cross-sectional area through which current flows, this confinement forces the same total current through a smaller area, increasing the effective AC resistance compared to the DC resistance. This is why high-frequency conductors are often plated or made hollow to save material without sacrificing performance.
- Does the skin effect occur with direct current (DC)?
- No, the skin effect is a direct consequence of time-varying electromagnetic fields. With steady DC (ω=0), the skin depth formula gives an infinite depth, meaning the current distributes uniformly across the conductor's cross-section (for a homogeneous material). The effect only becomes significant when the frequency is high enough that the skin depth is comparable to or smaller than the conductor's radius.
- What is a key limitation of this 1D exponential model?
- This model assumes a semi-infinite planar conductor, which is an excellent approximation for the flat surface of a large wire. However, for a cylindrical wire of finite radius, the current distribution is more complex, described by Bessel functions. The simple exponential decay is not perfectly accurate near the center of a round wire, especially when the wire radius is not much larger than the skin depth.
- How does the choice of conductor material impact the skin depth?
- Skin depth depends on both permeability (μ) and conductivity (σ). For a given frequency, a higher conductivity (like silver vs. copper) leads to a smaller skin depth, concentrating current more sharply. More significantly, ferromagnetic materials (like iron) have a much higher relative permeability (μᵣ >> 1), which dramatically reduces skin depth, making the skin effect extreme even at power-line frequencies.