Distributed shunt admittance

Dear everyone,
I found an equation about the relation between distributed shunt admittance and permittivity:

I have not seen this equation before. Can anyone show me where I can look for concept about this or relation equations? Thank.

For a mathematically correct equation, a length quantity is missing.

It would be definitely helpful if you briefly explain the meaning of "distributed shunt admittance" or tell where you found the quote.

Dear FvM,

As we know a transmission line can be modeled with series L (H/m) and shunt C (F/m) lump elements. And distributed shunt admittance is Y (S/m)= j*w*C (where w is angular frequency and C (F/m) is model lump element). And in a paper, the authors mention the above relation.

I only know the distributed capacitor model and epsilon have same unit (F/m).

I think it's always problematic to use a well-known formula sign like C or Y for a different quantity like characteristic or "distributed" capacitance. It would prefer a sign like δC or C'. But I see that some textbooks are using this ambiguous symbols.

Technically, the formula has the right unit. Presumed that ε really means permittivity and not a second equivocal quantity, there is a geometry factor linking ε and C'. In case of a coaxial line, you get

C' = 2 pi ε/ln(ro/ri)

so the geometry factor is 2 pi/ln(ro/ri).

I also think that the ε cannot be equal to distributed capacitance δC. So the equation may be incorrect. I'm not sure about this.

Anyway, thank FvM.