A 90, cm long solenoid has six layers of wind | vedclass

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(C) The total number of turns $N$ for $6$ layers, each with $450$ turns, is given by:$N = 6 	imes 450 = 2700$The number of turns per unit length $n$

Vedclass · Accepted Answer

$72$

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(C) The total number of turns $N$ for $6$ layers, each with $450$ turns, is given by:$N = 6 	imes 450 = 2700$The number of turns per unit length $n$ is calculated as:$n = \frac{N}{l} = \frac{2700}{90 	imes 10^{-2}\, m} = \frac{2700}{0.9}\, m^{-1} = 3000\, m^{-1}$The magnetic field $B$ inside a long solenoid near its centre is given by the formula:$B = \mu_{0} n I$Substituting the values $\mu_{0} = 4\pi 	imes 10^{-7}\, T\cdot m/A$, $n = 3000\, m^{-1}$, and $I = 6\, A$:$B = (4\pi 	imes 10^{-7}) 	imes 3000 	imes 6$$B = 72\pi 	imes 10^{-4}\, T$Since $1\, T = 10^4\, G$ (Gauss), we have:$B = 72\pi 	imes 10^{-4} 	imes 10^4\, G = 72\pi\, G$

$A$ $90\, cm$ long solenoid has six layers of windings of $450\, turns$ each. If the diameter of the solenoid is $2.2\, cm$ and the current carried is $6\, A$, then the magnitude of the magnetic field inside the solenoid, near its centre is: (in $\pi\, G$)

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