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

Two parallel plates of metal sandwich a dielectric pad of thickness d, forming an ideal

capacitor of capacitance C. The dielectric pad is elastic, having a spring constant k. If an

ideal battery of voltage V across its terminals is connected to the two plates of this

capacitor, the fractional change $ \frac{\delta{d}}{d} $ in the gap between the plates is

**2. Relevant equations**

$$C=\frac{\epsilon{A}}{d}$$

$$U=\frac{1}{2}CV^2$$

$$U=\frac{1}{2}k\delta{d}^2$$

**3. The attempt at a solution**

The Capacitance of the capacitor is $U=\frac{1}{2}CV^2$, when the dielectric is elastic the workdone in compressing/elongating the material of spring constant 'k' is $U=\frac{1}{2}k\delta{d}^2$, the fractional change in the energy of the capacitor is $\frac{1}{2}CV^2-\frac{1}{2}k\delta{d}^2$, I don't know what I have done is correct or not and I don't know how proceed from here as well. Please tell me whether my approach is not correct or give me a hint to solve the problem.