A glass plate completely fills the space between the plates of a parallel-plate capacitor of area 200 cm² and separation 0.885 mm. The capacitor remains connected to a 200 V battery. The dielectric constant of glass is 5. Neglect friction and the mass of the glass plate. Find the minimum work required to remove the glass plate, in µJ.
Physics · Capacitor
JEE Advanced

Question

A glass plate completely fills the space between the plates of a parallel-plate capacitor of area 200 cm² and separation 0.885 mm. The capacitor remains connected to a 200 V battery. The dielectric constant of glass is 5. Neglect friction and the mass of the glass plate. Find the minimum work required to remove the glass plate, in µJ.

Physics · Capacitor

G1 Physics · Accepted Answer

With the battery connected, the external work for removing the dielectric is W = ½V²(Cᵢ−C𝒇). Here Cᵢ = 5ε₀A/d and C𝒇 = ε₀A/d. Substituting A = 0.020 m², d = 0.885×10⁻³ m and V = 200 V gives W ≈ 16 µJ.