At steady state, the capacitor behaves like an open circuit in a DC circuit. The voltage across the capacitor will be equal to the voltage across the battery, and the charge \( Q \) on the capacitor is given by:
\[
Q = C \cdot V,
\]
where:
- \( C \) is the capacitance,
- \( V \) is the voltage across the capacitor (which is equal to the battery voltage).
Substitute the values for \( C \) and \( V \) to find the charge on the capacitor. The answer is \( 16 \, \mu C \).