Question 84: Magnetism and Matter

Question

A rod with circular cross-section area $$2 \mathrm{~cm}^{2}$$ and length $$40 \mathrm{~cm}$$ is wound uniformly with 400 turns of an insulated wire. If a current of $$0.4 \mathrm{~A}$$ flows in the wire windings, the total magnetic flux produced inside windings is $$4 \pi 	imes 10^{-6} \mathrm{~Wb}$$. The relative permeability of the rod is
(Given : Permeability of vacuum $$\mu_{0}=4 \pi 	imes 10^{-7} \mathrm{NA}^{-2}$$)

Accepted Answer

Magnetic field in the Solenoid,
$$
\begin{aligned}
& \mathrm{B}=\mu_0 \mu_r \mathrm{nI} \\
& 	ext { Magnetic flux, } \phi=\mathrm{N}(\mathrm{BA}) \\
& \phi=N\left(\mu_0 \mu_r n I Aight) \\
& \Rightarrow 4 \pi 	imes 10^{-6}=400\left(4 \pi 	imes 10^{-7} \mu_r 	imes \frac{400}{0.4} 	imes 0.4 	imes 2 	imes 10^{-4}ight) \\
& \Rightarrow \frac{1}{40}=\mu_r 	imes 8 	imes 10^{-2} \\
& \Rightarrow \mu_r=\frac{100}{320}=\frac{5}{16}
\end{aligned}
$$

Answer

$$\frac{5}{16}$$

Answer

125

Answer

$$\frac{32}{5}$$

Answer

12.5

Magnetism and Matter

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