Jackson's Electrodynamics. Question on Capacitance definition

[mateomy]

In Jackson's book he defines the capacitance of a conductor, "...the total charge on the conductor when it is maintained at unit potential, all other conductors being held at zero potential." I'm trying to get a more concrete definition in my head rather than the standard definition of capacitance being the ability to store charge. Can someone help me deconstruct Jackson's definition a bit further? From what my professor was drawing on the board, and from what he was saying ( in that, the capacitance is highly dependent on the geometry of the structure), I'm visualizing capacitance -from Jackson's- as a conductor in uniform charge distribution with respect to another nearby conductor. However, I'm also seeing this as very limited, if not wrong outright. I know somebody has the clarity I don't.

 

[Antiphon]

It's like this.

When you deposit charges onto a conductor there will be an accompanying change in the voltage of the conductor.

If the capacitance is low (like two widely separated conductors) then you'll get a big change in the voltage when you add the charge.

If the capacitance is large, you'll get a small change in the voltage.

The capacitance is only a function of the geometry (shape, layout and medium) of the plates.

Intuitively you would think that if you got a large voltage change then it took more energy to achieve that charge configuration. Intuition is confurmed by E=1/2 CV*V.

When conductors are widely separated the + and - charges on the plates provide less field cancellation of one another so it's harder (takes more work) to move charges in low-C systems.

As plates move closer, fields are reduced and charges are easier to move around.

Imagine a parallel-plate capacitor if 1 Peta-farad but only 1 square meter in area. The plates would have to be so close together that the electric field around it would be virtually nil. It would take very little work to add the first charge to such a large capacitor.

Hope that helps the deconstruction.

 

[mateomy]

That helps a lot. Thanks. I just want to have a really good visualization of these things while they're still visualize-able (if that makes sense).

 

[marcusl]

One qualification to the original post--the charge distribution on the conducting object need not be uniform. Charge will arrange itself to minimize the total electrostatic energy, which may mean more charges in some areas and fewer in others. The potential on the conductor is constant, however.

 

[Antiphon]

That helps a lot. Thanks. I just want to have a really good visualization of these things while they're still visualize-able (if that makes sense).

Things are pretty easy to visualize until you get to solenoidal electric fields. When you are used to conservative voltage potentials it's a little unsettling.