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  4. A rod with circular cross-section area 2 cm 2 and length 40 cm is wound uniformly with 400 turns of an insulated wire. If a current of 0.4 A flows in the wire windings, the total magnetic flux produced inside windings is 4 π × 10-6 Wb. The relative permeability of the rod is (Given: Permeability of vacuum μ0=4 π × 10-7 NA -2 )

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Q. A rod with circular cross-section area $2\, cm ^2$ and length $40 \,cm$ is wound uniformly with $400$ turns of an insulated wire. If a current of $0.4\, A$ flows in the wire windings, the total magnetic flux produced inside windings is $4 \pi \times 10^{-6}\, Wb$. The relative permeability of the rod is (Given : Permeability of vacuum $\mu_0=4 \pi \times 10^{-7}\, NA ^{-2}$ )

JEE MainJEE Main 2023Moving Charges and Magnetism

Solution:

$\phi=\mu_{ r } \mu_0 \frac{ N }{\ell} I \times A$
$ \mu_{ r }=125$