A closely wound solenoid 120 cm long has 4 l | vedclass

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(B) The magnetic field $B$ inside a long solenoid near its centre is given by the formula $B = \mu_0 n I$,where $n$ is the number of turns per unit le

Vedclass · Accepted Answer

$4.27 \pi 	imes 10^{-3} \ T$

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(B) The magnetic field $B$ inside a long solenoid near its centre is given by the formula $B = \mu_0 n I$,where $n$ is the number of turns per unit length.Given:Length of solenoid $L = 120 \ cm = 1.2 \ m$.Number of layers $= 4$.Turns per layer $= 400$.Total number of turns $N = 4 	imes 400 = 1600$.Current $I = 8.0 \ A$.Number of turns per unit length $n = \frac{N}{L} = \frac{1600}{1.2} = \frac{4000}{3} \ m^{-1}$.Substituting the values into the formula:$B = (4 \pi 	imes 10^{-7} \ T \cdot m/A) 	imes (\frac{4000}{3} \ m^{-1}) 	imes (8.0 \ A)$.$B = 4 \pi 	imes 10^{-7} 	imes \frac{32000}{3} \ T$.$B = \frac{128000}{3} \pi 	imes 10^{-7} \ T$.$B \approx 42666.67 \pi 	imes 10^{-7} \ T$.$B \approx 4.266 \pi 	imes 10^{-3} \ T$.Rounding to two decimal places,we get $B \approx 4.27 \pi 	imes 10^{-3} \ T$.

$A$ closely wound solenoid $120 \ cm$ long has $4$ layers of windings of $400$ turns each. The diameter of the solenoid is $1.8 \ cm$. If the current carried is $8.0 \ A$,estimate the magnitude of $B$ inside the solenoid near its centre.

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