A parallel plate capacitor is formed by two plates each of area \(30 \pi\, cm ^{2}\) separated by \(1\, mm\). A material of dielectric strength \(3.6 \times 10^{7} \,Vm ^{-1}\) is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is \(7 \times 10^{-6}\, C\), the value of dielectric constant of the material is \(\left\{ Use : \frac{1}{4 \pi \varepsilon_{0}}=9 \times 10^{9} Nm ^{2} C ^{-2}\right\}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.