A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of \(2 \times 10^5 \mathrm{~ms}^{-1}\). When the electric field is switched off, the proton moves along a circular path of radius 2 cm . The magnitude of electric field is \(x \times 10^4 \mathrm{~N} / \mathrm{C}\). The value of \(x\) is _______ Take the mass of the proton \(=1.6 \times 10^{-27} \mathrm{~kg}\).

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.