A parallel plate capacitor is formed by two plates, each of area 20 cm ^2 , separated by a distance of 1 mm . The space between the plates is completely filled with a material of dielectric constant 4 . If the maximum energy that can be stored in the capacitor without causing any dielectric breakdown is 0.1 J , the dielectric strength of the material is : [Use 1 4 ₀ = 9 10^9 N m ^2 C ⁻² ]

Step-by-step solution

The capacitance of the parallel plate capacitor is given by: C = k ₀ A d Given A = 20 10⁻⁴ m ^2 , d = 10⁻³ m , and k = 4 . Using ₀ = 1 36 10^9 F/m : C = 4 1 36 10^9 20 10⁻⁴ 10⁻³ = 20 9 10⁻¹⁰ F The maximum energy stored is U = 1 2 C V_ max ^2 . 0.1 = 1 2 ( 20 9 10⁻¹⁰ ) V_ max ^2 V_ max ^2 = 0.2 9 20 10⁻¹⁰ = 9 10^8 V_ max = 3 10^4 V The dielectric strength E_ max is the maximum electric field: E_ max = V_ max d = 3 10^4 10⁻³ = 3 10^7 V m ⁻¹ Answer: 3 10^7 V m ⁻¹