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Question

(C) The magnetic field $B$ inside a long solenoid is given by $B = \mu_n I = \mu_0 \mu_r n I$, where $n = N/L$ is the number of turns per unit length.

Vedclass · Accepted Answer

$125$

Vedclass · Answer

(C) The magnetic field $B$ inside a long solenoid is given by $B = \mu_n I = \mu_0 \mu_r n I$, where $n = N/L$ is the number of turns per unit length.Given: Area $A = 2 	ext{ cm}^2 = 2 	imes 10^{-4} 	ext{ m}^2$, Length $L = 40 	ext{ cm} = 0.4 	ext{ m}$, Number of turns $N = 400$, Current $I = 0.4 	ext{ A}$, Magnetic flux $\phi = 4\pi 	imes 10^{-6} 	ext{ Wb}$.The magnetic flux is $\phi = B \cdot A = \mu_0 \mu_r (N/L) I \cdot A$.Substituting the values: $4\pi 	imes 10^{-6} = (4\pi 	imes 10^{-7}) \cdot \mu_r \cdot (400 / 0.4) \cdot 0.4 \cdot (2 	imes 10^{-4})$.$4\pi 	imes 10^{-6} = (4\pi 	imes 10^{-7}) \cdot \mu_r \cdot 1000 \cdot 0.4 \cdot 2 	imes 10^{-4}$.$4\pi 	imes 10^{-6} = (4\pi 	imes 10^{-7}) \cdot \mu_r \cdot 8 	imes 10^{-2}$.$10^{-6} = 10^{-7} \cdot \mu_r \cdot 8 	imes 10^{-2}$.$10 = \mu_r \cdot 8 	imes 10^{-2}$.$\mu_r = 10 / (8 	imes 10^{-2}) = 1000 / 8 = 125$.

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