"charge" on a capacitor or battery

[JohnDenker]

In terms of honest-to-goodness charge, suppose a capacitor has a charge Q1 on the primary plate and a charge Q1 on the secondary plate. By all that's holy, the total charge on the capacitor is Q1+Q2.

• In typical applications, the honest-to-goodness charge Q1+Q2 is negligible.
• In typical applications, the quantity of interest is (Q1-Q2)/2. I call this the _gorge_. We can then speak of gorging and disgorging the capacitor.
• Unfortunately, there is a longstanding convention of calling (Q1-Q2)/2 the «charge». This is a fiasco. It conflicts with the fundamental physics definition of honest-to-goodness charge.

The book makes a valiant effort to skirt this issue ... but it eventually fails.

• Being technically, legally correct is not the same as being pedagogically clear.
• Equation 26.1 in section 26.5 on page 697 is not even correct. The equation has the right general form, but the variables it uses have been defined wrongly: q is defined to be always positive, no matter what the sign of the actual charge. This implies that the voltage is always positive, which is just completely wrong when the charge on the primary plate is negative. A capacitor is not a rectifier.

Suggestion: Here is the minimum change necessary to make things correct:

1. Introduce the concept of primary plate and secondary plate. It doesn't matter which plate is primary; just pick one and label it.
2. Add a prominent notice: In this chapter, when we speak of charging a capacitor, or speak of the charge Q in (or on) a capacitor, we mean there is a charge Q on the primary plate and a charge of -Q on the secondary plate. There is no law of physics that requires the two plates to have equal-and-opposite charges, but in practical applications people usually engineer things to make it so, or nearly so. Similar words apply to batteries as well.
3. Find all occurrences of the expression "magnitude of the charge" and replace them by "charge on the primary plate".

That's the least-intrusive change. One could imagine a number of more extensive changes.

[ericmazur]

I like your suggestion. Just one detail. Why make one plate the "primary" plate? In what sense is primary? Or more primary than the other plate??

How about just replacing ""magnitude of the charge" by "charge on/in the capacitor", given that the bold phrase defines that term?

[JohnDenker]

Instead of primary/secondary, one could introduce the terms obverse and reverse, or perhaps heads and tails. For electrolytic capacitors, there is a definite "+" terminal and "-" terminal, but for the simple capacitors considered here, the choice of orientation is arbitrary.

Instead of "magnitude of the charge" one could say simply "amount of charge". Rationale: getting rid of the word "magnitude" is the key issue. Adding "in/on the capacitor" adds specificity, but is tangential to the main issue, and may or may not be needed (depending on context).