A parallel-plate capacitor has plate separation d and capacitance C₁ with air between the plates. A metal sheet of thickness 2d/3 and the same area as the plates is inserted without touching either plate. The new capacitance is C₂. The ratio C₂: C₁ is:
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Question

A parallel-plate capacitor has plate separation d and capacitance C₁ with air between the plates. A metal sheet of thickness 2d/3 and the same area as the plates is inserted without touching either plate. The new capacitance is C₂. The ratio C₂: C₁ is:

Options

G1 Physics · Accepted Answer

For a metal slab of thickness t inserted between capacitor plates, the effective separation is d(eff) = d − t because electric field inside the metal is zero. Here, t = 2d/3 So, d(eff) = d − 2d/3 = d/3 Hence, C₂ = ε₀A/(d/3) = 3ε₀A/d But, C₁ = ε₀A/d Therefore, C₂/C₁ = 3 Hence option B follows.

A parallel-plate capacitor has plate separation d and capacitance C₁ with air between the plates. A metal sheet of thickness 2d/3 and the same area as the plates is inserted without touching either plate. The new capacitance is C₂. The ratio C₂:C₁ is: