I Induction heating vs Current heaing

[artis]

I've been thinking and can't come up with a satisfying answer. Would there be a difference in the amount of heat generated in a given time in a metal rod if it was heated by
a) induction
b) current passing through the same length of rod

Given that the current is the same amperage and frequency in both cases, also not taking into account the losses in current in the induction case.

So let's say you use 20kHz at 10 amps in one situation you simply pass that current down a metal rod , the current runs on the outer surface of the rod at the skin depth of the frequency given.
In the other case the same current runs through a coil creating a B field which then penetrates the metal rod to a skin depth.

So would there be any differences?
Are the skin depths the same both for the current through rod as well as B field penetrating rod case?

What about the mechanism for heating, in the current case it is the motion of electrons interacting with the atomic structure but in the induction case it also seems the same only due to eddy currents. The heat passed deeper than skin depth is then simply due to secondary interactions caused by the skin depth movement of electrons?

 

[anuttarasammyak]

a) induction is interpreted in effect as generated induction current. Since a) and b) are both currents, I think their effects are compared with how much current they experience.