A capacitor $C_1 = 4.0\ \mu\text{F}$ holds a charge of $60\ \mu\text{C}$. An uncharged capacitor $C_2 = 2.0\ \mu\text{F}$, a $30\ \text{V}$ battery and an open switch are joined to it in one loop, as in the figure. The positive plate of $C_1$ faces the positive terminal of the battery. Its negative plate is joined to $C_2$, and the other plate of $C_2$ goes to the negative terminal through the switch. The switch is now closed, and the charges settle. How much charge passes through the battery? Give the answer in $\text{μC}$.

Fig. 1: A single loop. A 30 V battery, with its positive terminal on the right, is joined to capacitor C1 of 4.0 microfarads, whose positive plate, carrying plus 60 microcoulombs, faces the battery and whose other plate carries minus 60 microcoulombs. That plate is joined to an uncharged capacitor C2 of 2.0 microfarads. The other plate of C2 goes through an open switch S back to the negative terminal of the battery.