A parallel plate capacitor is formed by two plates each of area 30 π cm 2 separated by 1 mm . A material of dielectric strength 3 . 6 × 10 7 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 dielectric constant of the material is : [Use 1 4 π ε o = 9 × 10 9 N m 2 C - 2 ]

Step-by-step solution

The dielectric strength given is 3 . 6 × 10 7   V   m - 1 .and the separation is 1   mm . Therefore, maximum potential difference that can be applied will be, V m a x = 3 . 6 × 10 7 × d . Now, C = q m a x V m a x ⇒ k ε 0 A d = 7 × 10 - 7 3 . 6 × 10 7 × d k = d ε 0 × 30 π × 10 - 4 × 7 × 10 - 7 3 . 6 × 10 7 × d = 2 . 33