Comparing inductance and capacitance: Analogy to charge

[greypilgrim]

Hi.
Inductance and capacitance have many analogies, both conceptually and formally. A capacitor connected to a voltage source carries the charge $Q=C\cdot V$. The analogous equation for inductance is $n\cdot \Phi=L\cdot I$.

Charge is physical, it's proportional to the number of excess electrons on one plate. But what exactly is $n\cdot \Phi$? I know what the magnetic flux is, but I wonder if there's a more tangible interpretation analogous to charge.

 

[Baluncore]

Energy is a fundamental so you might look at the parallel from that viewpoint.

For a capacitor; E = ½ · C · V²
Q = C · V
C = Q / V; the slope of the line dQ/dV = C.
E = ½ · Q · V; the area under the line is the energy.

For an inductor E = ½ · L · I²
Φ = L· I
L = Φ / I; the slope of the line dΦ/dI = L.
E = ½ · Φ · I; the area under the line is the energy.

 

[David Lewis]

But what exactly is n⋅Φn\cdot \Phi?

Current times inductance.
Inductance tells you how good a conductor is at generating a magnetic field when current flows through it.