Question

Consider the situation shown in figure (31-E31). The plates of the capacitor have plate area A and are clamped in the laboratory. The dielectric slab is released from rest with a length a inside the capacitor. Neglecting any effect of friction or gravity, show that the slab will execute periodic motion and find its time period.

Answer 1

Capacitance of the portion with dielectrics,

C₁ = Kε₀A/ld

Capacitance of the portion without dielectrics,

C₂ = ε₀(l - a)A/ld

Consider the motion of dielectric in the capacitor.

Let it further move a distance dx, which causes an increase of capacitance by dc

∴ dQ = (dc)E

The work done by the battery dw = Vdg = E (dc) E = E² dc

Let force acting on it be f

∴ Work done by the force during the displacement, dx = fdx

∴ Increase in energy stored in the capacitor