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(B) To calculate the mutual inductance $M$ of the system,we use the principle of reciprocity,which states that $M_{12} = M_{21} = M$.Let a current $I_

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Mutual inductance of the solenoids is $\pi \mu_{0} r^{2} n N l$.

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(B) To calculate the mutual inductance $M$ of the system,we use the principle of reciprocity,which states that $M_{12} = M_{21} = M$.Let a current $I_{1}$ flow through the long outer solenoid (solenoid $1$). The magnetic field produced by this solenoid inside it is uniform and given by $B = \mu_{0} N I_{1}$.The magnetic flux $\phi_{21}$ linked with the short inner solenoid (solenoid $2$) is the product of the number of turns in the inner solenoid,the magnetic field,and the cross-sectional area of the inner solenoid.Number of turns in the inner solenoid = $n 	imes l$.Area of the inner solenoid = $\pi r^{2}$.Therefore,$\phi_{21} = (n l) 	imes B 	imes (\pi r^{2}) = (n l) 	imes (\mu_{0} N I_{1}) 	imes (\pi r^{2})$.By definition,$\phi_{21} = M I_{1}$.Comparing the two expressions,we get $M = \mu_{0} N n l \pi r^{2} = \pi \mu_{0} r^{2} n N l$.

$A$ short solenoid (length $l$ and radius $r$ with $n$ turns per unit length) lies well inside and on the axis of a very long,coaxial solenoid (length $L$,radius $R$ and $N$ turns per unit length,with $R > r$). Current $I$ flows in the short solenoid. Choose the correct statement.

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