A parallel plate capacitor is formed by two plates each of area 30π cm², separated by 1 mm. A material of dielectric strength 3.6×10⁷ V m⁻¹ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is 7×10⁻⁶ C, the value of the…

Question

A parallel plate capacitor is formed by two plates each of area 30π cm², separated by 1 mm. A material of dielectric strength 3.6×10⁷ V m⁻¹ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is 7×10⁻⁶ C, the value of the dielectric constant of the material is [Use1/(4πε₀)=9×10⁹ N m² C⁻²]

Accepted Answer

(4) 2.33. Breakdown sets the largest field the material can hold, so Vₘₐₓ=Eₘₐₓd=3.6×10⁷×10⁻³=3.6×10⁴ V. C=(Qₘₐₓ)/(Vₘₐₓ)=(7×10⁻⁶)/(3.6×10⁴)=1.944×10⁻¹⁰ F. The air value is (ε₀A)/d with ε₀=(10⁻⁹)/(36π) and A=30π×10⁻⁴ m²: (ε₀A)/d=(10⁻⁹×30π×10⁻⁴)/(36π×10⁻³)=8.33×10⁻¹¹ F. K=(1.944×10⁻¹⁰)/(8.33×10⁻¹¹)=7/3=2.33.

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