A particle carrying a charge equal to 1000 times the charge on an electron, is rotating one rotation per second in a circular path of radius ' r ' m . If the magnetic field produced at the centre of the path is \(x\) times the permeability of vacuum, the radius ' \(r\) ' in \(m\) is
\(\left[\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\right] \quad\left[\mathrm{x}=2 \times 10^{-16}\right]\)

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.