Question

Two charged capacitors have their outer plates fixed and inner plates connected by a spring of force constant $k$ . The magnitude of charge on each capacitor is $q$ and sign of charge is shown in figure. Find the extension in the spring at equilibrium.

• A. $\frac{q^{2}}{2 A \epsilon _{0} k}$
• B. $\frac{q^{2}}{4 A \epsilon _{0} k}$
• C. $\frac{q^{2}}{A \epsilon _{0} k}$
• D. zero

Answer 1

Answer: (A)

We know that spring force $F=kx$ will balance electrostatic force of attraction.
Therefore, $\frac{q^{2}}{2 A \epsilon _{0}}=kx$
$\Rightarrow x=\frac{q^{2}}{2 A \epsilon _{0} k}$