# Charge on capacitor connected between spheres

**1. The problem statement, all variables and given/known data**

Two metallic spheres, each of radius R having charges 2Q and Q are joined through a capacitor of capacitance C as shown in the figure. Assuming R<<d, the charge on the capacitor long time after the key K is closed is:

(Ans: ##\dfrac{Q}{2+\frac{4\pi \epsilon_0 R}{C}}##)

**2. Relevant equations**

**3. The attempt at a solution**

The final distribution of charges should be as shown in attachment 2.

From conservation of energy:

$$\frac{(2Q)^2}{2x}+\frac{Q^2}{2x}=\frac{(2Q-q)^2}{2x}+\frac{q^2}{2C}+\frac{(Q+q)^2}{2x}$$

where ##x=4\pi \epsilon_0 R##.

Solving the above doesn’t give me the right answer. :confused:

Any help is appreciated. Thanks!

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