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.

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. <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-qnndneqrjkqivh1u.jpg" /> (A) (q2/2 A ϵ 0 k) (B) (q2/4 A ϵ 0 k) (C) (q2/A ϵ 0 k) (D) zero

Tardigrade Admin · Accepted Answer

We know that spring force F=kx will balance electrostatic force of attraction. Therefore, (q2/2 A ϵ 0)=kx ⇒ x=(q2/2 A ϵ 0 k)

Q. 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.

$\frac{q ^{2}}{2 A ϵ _{0} k}$

$\frac{q ^{2}}{4 A ϵ _{0} k}$

$\frac{q ^{2}}{A ϵ _{0} k}$

zero

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

Q. 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.

2Aϵ0​kq2​

4Aϵ0​kq2​

Aϵ0​kq2​