Question

Two identical metal plates each of area A arranged parallel to each other as shown. The lower plate is held fixed and the upper plate is connected at its middle to one end of a spring of force constant 'k'. The other end of the spring is attached to a fixed support. When either of the plates has no charge, the equilibrium distance between them is d. Now the switch is closed to apply a voltage between the plates. What maximum voltage v in this way can be applied between the plates, so that they would not touch each other (ignore force of gravity)?

• A. $\sqrt{\frac{2k{d}^3}{3{\epsilon }_{0}A}}$
• B. $\frac{2}{3}\sqrt{\frac{2k{d}^3}{3{\epsilon }_{0}A}}$
• C. $\frac{2}{3}\sqrt{\frac{k{d}^3}{{\epsilon }_{0}A}}$
• D. $\sqrt{\frac{k{d}^3}{{\epsilon }_{0}A}}$

Answer 1

The correct option is A $\sqrt{\frac{2k{d}^3}{3{\epsilon }_{0}A}}$