Question

The parallel-plate air capacitor shown in fig consists of two horizontal conducting plates of equal area A. The bottom plate rests on a fixed support and the top plate is suspended by four springs with spring constant k, positioned at each of the four corners of the plate as shown in Fig. When uncharged, the plates are separated by a distance $z_0$. A battery is connected to the plates and produces a potential difference V between them. This causes the plate separation to decrease to z. Neglect any fringing effects. Find the condition of stable equilibrium :

• A. z shall have positive root
• B. z shall negative root
• C. no dependence on value of z
• D. none of these

Answer 1

The correct option is B z shall negative root

For stable equilibrium the potential should be minimum. i.e, $V=\frac{1}{2}k(z_0+z{)}^2$ and$\frac{dV}{dz}=0$

As z is decreases so it shall have negative root.