I have a question about the skin effect on inductors, I would like to know why the skin effect will reduce the inductance? You could see from the below figure, in the high frequency the inductance was reduced, but the resistance will be increased. Could someone give me some suggestions, thanks?
In addition to the field explanation, there's a very basic argument from just the fact that an inductor is a real 2-terminal element: as a consequence of the impedance being analytical, the real and complex elements obey Kramers-Kronig relations. Basically, a lossy inductance is necessarily a decreasing inductance; the impedance is still going up with frequency, but a little slower than proportionally so (\$\left|Z\right| < j \omega L\$). The amount by which it's slower, gives the resistance fraction. (For example, if R = X_L, the slope (on log-log plot) is half, or Z ~ sqrt(F), a diffusion element.)
If impedance is rising faster than proportional (or falling faster than inversely for capacitors), it can only happen within a narrow band (approaching a resonance), as is the case near SRF (self resonant frequency).
(This is not a complete description of what impedance can do as a function of frequency, but is sufficient for commercial inductors, which can be modeled as a lossy inductor with some capacitance to cover DC to a bit beyond SRF, or including other more complex behavior at high frequencies which may not be very important to model anyway.)
The phenomenon that causes skin effect forces the curent to flow in the outer layers of the conductor. Because the current is flowing in the outer layers (and not uniformly throughout the conductor cross-section), there is less internal flux coupling, and in fact less total magnetic flux is generated (in the limit none inside the conductor). This directly means there is less inductance.