A long wire lies along \(X\)-axis and carries a current of \(40 \mathrm{~A}\) in positive \(x\)-direction. A second long wire is perpendicular to the \(x y\)-plane, passes through point \((3.0 \mathrm{~m}) \hat{j}\) and carries a current along positive \(z\)-direction. If the magnitude of resultant magnetic field at the point \((2.0 \mathrm{~m}) \hat{j}\) \(R=5 \times 10^{-6} \mathrm{~T}\) then the current in the second wire is
(Permeability of free space, \(\mu_0=4 \pi \times 10^{-7}\) SI unit)

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.