A parallel-plate capacitor is formed by two plates, each of area 30π cm², separated by 1 mm. A dielectric of strength 3.6×10⁷ V m⁻¹ fills the space. If the maximum charge that can be stored without dielectric breakdown is 7×10⁻⁶ C, find the dielectric constant. Use 1/(4πε₀) = 9×10⁹ N m² C⁻².
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Question

A parallel-plate capacitor is formed by two plates, each of area 30π cm², separated by 1 mm. A dielectric of strength 3.6×10⁷ V m⁻¹ fills the space. If the maximum charge that can be stored without dielectric breakdown is 7×10⁻⁶ C, find the dielectric constant. Use 1/(4πε₀) = 9×10⁹ N m² C⁻².

Options

G1 Physics · Accepted Answer

Breakdown occurs at electric field 3.6×10⁷ V/m. The maximum charge satisfies Q = ε₀KAE. Substituting Q = 7×10⁻⁶ C and E = 3.6×10⁷ V/m gives K ≈ 2.33, hence option D.