Answer:

Introduction:
In this problem, we are given a parallel plate capacitor with charges of 4Q and -2Q. The capacitor is then connected across an uncharged capacitor of the same capacitance as the first one. We need to find the final potential difference between the plates of the first capacitor.

Explanation:
When the parallel plate capacitor is connected to the uncharged capacitor, the charge on the first capacitor will get shared between the two capacitors in such a way that the potential difference across the two capacitors remains the same.

Step 1: Calculate the initial potential difference across the plates of the first capacitor.

The potential difference across the plates of a capacitor is given by:

V = Q/C

where Q is the charge on the capacitor and C is the capacitance.

Therefore, the initial potential difference across the plates of the first capacitor is:

V1 = 4Q/C

Step 2: Calculate the charge on the uncharged capacitor.

When the two capacitors are connected in parallel, the charges on the two capacitors will get shared in such a way that the potential difference across the two capacitors remains the same. Since the capacitors are of the same capacitance, the charges on the two capacitors will be equal.

Let the charge on the uncharged capacitor be Q2.

Then, the charge on the first capacitor will be Q1 = 4Q - Q2.

Since the total charge is conserved, we have:

Q1 + Q2 = 4Q

Substituting Q1, we get:

(4Q - Q2) + Q2 = 4Q

Simplifying, we get:

Q2 = 2Q

Therefore, the charge on the uncharged capacitor is 2Q.

Step 3: Calculate the final potential difference across the plates of the first capacitor.

When the two capacitors are connected in parallel, the potential difference across the two capacitors will be the same. Therefore, the potential difference across the plates of the first capacitor will be:

V1' = Q1/C = (4Q - Q2)/C = (4Q - 2Q)/C = 2Q/C

Therefore, the final potential difference across the plates of the first capacitor is 2Q/C.

Conclusion:
In conclusion, the final potential difference across the plates of the first capacitor is 2Q/C. When the two capacitors are connected in parallel, the charge on the first capacitor gets shared between the two capacitors in such a way that the potential difference across the two capacitors remains the same.

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