A rod with a circular cross-section area \(2\) cm\(^2\) and length \(40\) cm is wound uniformly with \(400\) turns of an insulated wire. If a current \(0.4\) A flows in the wire winding, the total magnetic flux produced inside the winding is \(4π\times 10^{-6}\) Wb. The relative permeability of the rod is (Given permeability of vacuum \(μ_0 = 4π\times 10^{-7}\) N m A\(^{-2}\))
Step 1: Plan:
Compare with the flux the same coil would give in vacuum.
Step 2: Steps:
Without the rod, the flux would be $\mu_0nIA = 1.6\pi\times10^{-4}\times2\times10^{-4} = 3.2\pi\times10^{-8}$ Wb.
The actual flux is $4\pi\times10^{-6}$ Wb. The ratio $\frac{4\pi\times10^{-6}}{3.2\pi\times10^{-8}} = 125$ is the relative permeability.
Final Answer:
The relative permeability of the rod is $125$, option (C).
\[ \boxed{125} \]