[Physics] charge a capacitor using 2 batteries


1 capacitor, 2 separate batteries (Battery A and Battery B).
Connect A+ to one side of the capacitor and B- to the other side of the capacitor.
A and B are not connected, there is no closed circuit.
looking like:


Can the capacitor be charged this way or not? if not, why?

Best Answer

No. Batteries supply potential difference.

The positive terminal of A(I'll call it A+) is at a higher potential than the negative terminal of A(A-). The same goes for B. However, we don't know if A- and B+ are at the same potential, so we can't conclude that A+ is at a higher potential than B-.

In fact, A+ and B- are at the same potential, as it is the lowest energy configuration of this system.

For a capacitor to work, there needs to be a potential difference across its ends. Here, there isn't.

Besides, a battery only works when charge is being drawn/added from/to both terminals. Electrostatic repulsion will not let the battery supply charge from just one terminal. Don't look at a battery as a producer of charge. Look at it as a separator of charge. For every positive charge A shoots out of its positive terminal, there will be a negative charge that gets stuck on its negative terminal; which will work to prevent more negative charges from accumulating on A-. If negative charge can't accumulate on A-, then A+ will stop shooting out charges. This happens very quickly -- you won't be able to measure the amount of charge that A+ released.

However, if you connect A- and B+, then A- and B+ will be at the same potential, and A+ will be at a higher potential that B-, and the capacitor will charge.