Published by:
CGP EDU Academic Team
Published on: September 12, 2026
A plate A of a parallel-plate capacitor is fixed, while a plate B is attached to the wall by a spring and can move, remaining parallel to the plate A (Fig.). After the key K is closed, the plate B starts moving and comes to rest in a new equilibrium position. The initial equilibrium separation d between the plates decreases in this case by 10%.
What will be the decrease in the equilibrium separation between the plates if the key K is closed for such a short time that the plate B cannot be shifted noticeably?
Text Solution
Verified by ExpertsThe correct answer is:
B
Step 1: Understand that closing key K charges the capacitor while maintaining the distance d between the plates initially.
Step 2: The charge stored is given by Q = CV, where C is the capacitance, and V is the voltage.
Step 3: Upon closing the switch briefly, the electric field E increases, prompting the plate B to move.
Step 4: The force on plate B due to the electric field is F = QE, which results in the movement of the plate.
Step 5: To find the new equilibrium position, we note that the system-energy considerations imply that the force exerted by the electric field balances the spring force.
Step 6: With a 10% decrease in distance d to the new position, we can conclude the equilibrium separation decreases.
Therefore, for a brief closure of K, the decrease is negligible, so the answer is B.
Step 2: The charge stored is given by Q = CV, where C is the capacitance, and V is the voltage.
Step 3: Upon closing the switch briefly, the electric field E increases, prompting the plate B to move.
Step 4: The force on plate B due to the electric field is F = QE, which results in the movement of the plate.
Step 5: To find the new equilibrium position, we note that the system-energy considerations imply that the force exerted by the electric field balances the spring force.
Step 6: With a 10% decrease in distance d to the new position, we can conclude the equilibrium separation decreases.
Therefore, for a brief closure of K, the decrease is negligible, so the answer is B.
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