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(C) The magnetic field $B$ at the center of a long solenoid is given by the formula $B = \mu_0 n' i$,where $n'$ is the number of turns per unit length

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Independent of $D$

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(C) The magnetic field $B$ at the center of a long solenoid is given by the formula $B = \mu_0 n' i$,where $n'$ is the number of turns per unit length.In this problem,there are $n$ layers of windings,and each layer has $N$ turns over a length $L$.Therefore,the total number of turns per unit length is $n' = \frac{n 	imes N}{L}$.Substituting this into the formula,we get $B = \mu_0 \left( \frac{nN}{L} ight) i$.As we can see from the expression,the magnetic field $B$ depends on the permeability of free space $\mu_0$,the number of layers $n$,the number of turns $N$,the current $i$,and the length $L$.It does not depend on the diameter $D$ of the solenoid.Thus,the magnetic field is independent of $D$.

List-$I$	List-$II$
$(1)$ Planck's constant	$(i)$ $[ML^{-1} T^{-2}]$
$(2)$ Gravitational constant	(ii) $[ML^{-1} T^{-1}]$
$(3)$ Bulk modulus	(iii) $[ML^2 T^{-1}]$
$(4)$ Coefficient of viscosity	(iv) $[M^{-1} L^3 T^{-2}]$

$A$ long solenoid of length $L$ has a mean diameter $D$. It has $n$ layers of windings of $N$ turns each. If it carries a current $i$,the magnetic field at its centre will be

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