A rod with circular cross-section area 2 cm ^ 2 and length 40cm is...

Magnetic flux is given by $ϕ = NBA$, here, $N$ is number of turns, $B$ is magnetic field and $A$ is area.

Given here, $ϕ = 4\pi \times {10}^{- 6}Wb, A = 2{cm}^{2}, N = 400, I = 0 . 4A$.

Putting the values,

$ϕ = 400 \times \left({\mu}_{r}{\mu}_{0}nI\right) \times A$

$⇒ 4\pi \times {10}^{- 6} = 400\left[{\mu}_{r} \times 4\pi \times {10}^{- 7} \times \dfrac{400}{0 . 4} \times 0 . 4\right] \times 2 \times {10}^{- 4}$

$⇒ {\mu}_{r} = 125$