Only if we suppose the battery is not connected.
But in case of being battery connected then
Q2/Q1 = (A1+A2)/A1
So Q2/(A1+A2) = Q1/A1
i.e. final charge density = initial charge density.
{ Q1,Q2 are supposed initial and final charge on plates respectively }
If a battery is connected while attaching two uncharged plates of area A2. The Charge on the plates will simply increase as capacitance is increased (due to increase in area) if and only if we consider potential from battery remains constant.
For question no 2.
If battery is not connected
We can proceed like this
charge density on A1 = charge density on A2.
So let q charge displaces from A1 to A2
Charge on A1 = Q1-q
Charge on A2 = q
If battery is connected
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