Simulation · Physics · Class 12

A parallel plate capacitor on a 100 V battery

From the lesson Effect of dielectric on capacitance in Electrostatic Potential and Capacitance. Change the values and watch what happens.

The idea behind it

NCERT §2.13

With vacuum between the plates, E₀ = σ/ε₀, V₀ = E₀d and C₀ = ε₀A/d.
A dielectric filling the gap is polarised; its bound surface charges ±σₚ cut the effective charge density to σ − σₚ, so E = (σ − σₚ)/ε₀.
For a linear dielectric σ − σₚ = σ/K, where K > 1 is the dielectric constant. The field and V both fall by the factor K for the same charge.
Hence C = Kε₀A/d = KC₀. The dielectric constant is the factor by which capacitance grows when the dielectric fills the space fully.
Permittivity of the medium ε = ε₀K; K = ε/ε₀ is dimensionless. For vacuum K = 1.
C = KC₀ holds for a capacitor of any shape, so it can serve as the definition of K.
Slab partly filling the gap: a slab of constant K and thickness 3d/4 (full plate area) makes V = E₀d(K + 3)/(4K) for the same charge, so C = 4KC₀/(K + 3).

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