A thin metallic wire having cross sectional area of \(10^{-4} \mathrm{~m}^2\) is used to make a ring of radius \(30 \mathrm{~cm}\). A positive charge of \(2 \pi \mathrm{C}\) is uniformly distributed over the ring, while another positive charge of \(30\) \(\mathrm{pC}\) is kept at the centre of the ring. The tension in the ring is__________ \(\mathrm{N}\); provided that the ring does not get deformed (neglect the influence of gravity). (given, \(\frac{1}{4 \pi \epsilon_0}=9 \times 10^9 \mathrm{SI}\) units)

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.