Question

The electrostatic force (\(F\)) between the metal plates of an isolated parallel plate capacitor (\(C\)) having a charge \(Q\) and area \(A\) is (\(d\) = distance between the plates)

• A. \(F\propto \sqrt{d}\)
• B. \(F\propto d\)
• C. independent of \(d\)
• D. \(F\propto \frac{1}{d}\)

Hint:

For fixed charge, the field of one plate does not depend on the separation, so the force on the other plate is independent of d.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
The field of one plate with surface charge density \(\sigma\) is \(E=\frac{\sigma}{2\epsilon_{0}}=\frac{Q}{2\epsilon_{0}A}\).

Step 2: Force on the Other Plate
\(F=QE=\frac{Q^{2}}{2\epsilon_{0}A}\).

Step 3: Compare the options
This contains only \(Q\), \(A\) and \(\epsilon_{0}\), all fixed, so the force does not depend on \(d\).

Final Answer:
The force is independent of the distance between the plates. \[ \boxed{\text{(C) }\text{independent of }d} \]