If a slab of insulating material (conceptual). 4 10⁻³ ~m thick is introduced between the plates of a parallel plate capacitor, the separation between the plates has to be increased by 3.5 10⁻³ ~m to restore the capacity to original value. The dielectric constant of the material will be

Step-by-step solution

Let t be the thickness of the dielectric slab and K is the dielectric constant. So, the increase in the distance of separation between the plates due to dielectric is given as aligned x &=t- t K &=t (1- 1 k ) aligned Given, x=3.5 10⁻³ ~m , t=4 10⁻³ ~m Substituting the given values in the above equation, we get 1- 1 k = x t = 3.5 10⁻³ 4 10⁻³ = 3.5 4 or 1 k =1- 3.5 4 = 0.5 4 or k=8