$A$ coil of radius $1\, cm$ and $100$ turns is placed in the middle of a long solenoid of radius $5\, cm$ having $5\, turns/cm$, with its axis parallel to the axis of the solenoid. The mutual inductance in millihenry is:

Two coils have a mutual inductance $0.003 \ H$. The current changes in the first coil according to the equation $I = I_0 \sin \omega t$, where $I_0 = 8 \ A$ and $\omega = 100 \pi \ rad \ s^{-1}$. The maximum value of e.m.f. in the second coil is (in $\pi \ V$)

$A$ solenoid of length $0.30 \, m$ has $2000$ turns. The area of its cross-section is $1.2 \times 10^{-3} \, m^2$. Around its central section,a coil of $300$ turns is wound. If an initial current of $2 \, A$ in the solenoid is reversed in $0.25 \, s$,then the $e.m.f.$ induced in the coil is:

Explain mutual induction and derive the equation for mutual $emf$.

$A$ circular loop of radius $0.3 \, cm$ lies parallel to a much bigger circular loop of radius $20 \, cm$. The centre of the small loop is on the axis of the bigger loop. The distance between their centres is $15 \, cm$. If a current of $20 \, A$ flows through the smaller loop,then the flux linked with the bigger loop is:

Two coils of self-inductance $25 \ mH$ and $9 \ mH$ are placed close together such that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is (in $mH$)