If N is the number of turns in a coil,the val | vedclass

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(D) The self-inductance $L$ of a coil is defined as $L = \frac{N \phi}{i}$,where $N$ is the number of turns,$\phi$ is the magnetic flux through each t

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$N^2$

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(D) The self-inductance $L$ of a coil is defined as $L = \frac{N \phi}{i}$,where $N$ is the number of turns,$\phi$ is the magnetic flux through each turn,and $i$ is the current.For a solenoid,the magnetic flux $\phi$ is given by $\phi = B A$,where $B$ is the magnetic field and $A$ is the cross-sectional area.The magnetic field $B$ inside a solenoid is $B = \mu_0 n i = \frac{\mu_0 N i}{l}$,where $n$ is the number of turns per unit length $(n = N/l)$ and $l$ is the length of the solenoid.Substituting $B$ into the flux equation: $\phi = \left( \frac{\mu_0 N i}{l} \right) A$.Now,substituting $\phi$ into the expression for $L$: $L = \frac{N}{i} \left( \frac{\mu_0 N i A}{l} \right) = \frac{\mu_0 N^2 A}{l}$.Thus,the self-inductance $L$ is proportional to $N^2$.

If $N$ is the number of turns in a coil,the value of self-inductance varies as

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