Question

[Key Concept: In a dielectric the displacement current is I_d = Kε₀ dΦ_E/dt.]

From formula

$$I_{d} = \frac{\in_{0} \in_{r}d\phi_{E}}{dt}$$

$\because\frac{d\phi_{E}}{dt} = \frac{d}{dt}\left( 8 \times 10^{3} \times t^{4} \right) = 32000t^{3}$

At $t = 20 \times 10^{- 3}$ second

$$\frac{d\phi_{E}}{dt} = 32000 \times \left( 20 \times 10^{- 3} \right)^{3} = 0.256$$

Using all the values in formula of displacement current

$I_{d} = \in_{0} \in_{r}\frac{d\phi_{E}}{dt}$

$12.5 \times 10^{- 12} = \left( 8.85 \times 10^{- 12} \right) \in_{r} \times 0.256$

$$\in_{r} = 5.52 Correct\ option\ is\ (b)\ 5.52$$