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Suppose i have two very long parallel metal plates and i give them charges $Q_1$ and $Q_2 $respectively with $Q_1>Q_2$.The charges on the inner faces will be $(Q1-Q_2)/2 \ and \ -(Q_1-Q_2)/2$.If i connect these plates with a battery it is observed that the charges on the outer surface of the plates does not change and only the charges on the inner face may change. Why is it so?

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As we know that for isolated system of parallel plates, the charge on the outer surface of the first and last plate is $\displaystyle\frac{\sum Q_i}{2}$ where $\sum Q_i$ is sum of charges on all the plates.

Now, after connecting these system to a battery, the battery supplies some charge due to which distribution of charges takes place and the same amount of charge is given out by the system (here the capacitor). Hence, there is no net transfer of charge and the quantity $\sum Q_i$ remains the same. So, the amount of charge on the outer surface remains same.

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