A parallel-plate capacitor of initial capacitance is connected to an ideal battery…
PHYSICS · Multi-part · CBSE · Physics · Electrostatic Potential and Capacitance · Electrostatic Potential and Capacitance
Problem
A parallel-plate capacitor of initial capacitance C0 is connected to an ideal battery that maintains a constant potential difference V. A dielectric slab of thickness equal to the plate separation and dielectric constant κ is slowly inserted between the plates from one side until it completely fills the space. Assume the slab slides in parallel to the plates so that, during insertion, one portion of the capacitor is filled with dielectric while the remainder contains air.
(a) Treating the arrangement at an intermediate stage as two capacitors side by side, derive an expression for the equivalent capacitance when the slab has been inserted a fraction x of the plate area (0≤x≤1).
(b) Obtain expressions for the energy stored in the capacitor before insertion and after the slab fully fills the space.
(c) Determine the net work done by an external agent in inserting the slab completely. Express your answer in terms of C0, V, and κ.
(d) State whether the external agent must do positive work, negative work, or no work, and explain the physical origin of the force acting on the slab.