A proton moving with a velocity of \(8 \times 10^5 \mathrm{~ms}^{-1}\) enters a uniform magnetic field normal to the direction of the magnetic field. If the radius of the circular path of the proton in the magnetic field is 8.3 cm, then the magnitude of the magnetic field is \(\left(\right.\) Charge of proton \(=1.6 \times 10^{-19} \mathrm{C}\) and mass of the proton \(\left.=1.66 \times 10^{-27} \mathrm{~kg}\right)\)

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.