But ferrites aren't soft materials.
Ferrites are soft or hard depends on their magnetic properties. Yes, they are not "soft" materials, because you will take lots of time to cut one.
Just like soft iron does not store magnetism, it produces lots of induction but "retentivity" or "coercivity" is small.
Same is the case for "soft ferrites".
They are metal oxides (iron, nickel, etc etc) and are produced by sintering and heat treatment. Mechanically they are hard and brittle. Handle with care.
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Much akin to wire having self induction but in this case capacitance
More important than their self-capacitance, is the inter turn capacitance.
In this case you are considering two turns of the same solenoid as a capacitor but they are electrically connected.
Just like a straight wire has some self inuctance but what you are perhaps interested is the inductance of the solenoid.
Both depend on the geometry and less on the size of the wire.