$A$ long straight wire is placed along the axis of a circular ring of radius $R$. The mutual inductance of this system is

The number of turns of primary and secondary coils of a transformer are $5$ and $10$ respectively and the mutual inductance of the transformer is $25\,H$. Now,the number of turns in the primary and secondary of the transformer are made $10$ and $5$ respectively. The mutual inductance of the transformer in henry will be:

Two coils of self-inductance $100\,mH$ and $400\,mH$ are placed very close to each other. Find the maximum mutual inductance between the two. (The current value is irrelevant to the calculation of mutual inductance).

$A$ varying current at the rate of $3 \, A/s$ in a coil generates an $e.m.f.$ of $8 \, mV$ in a nearby coil. The mutual inductance of the two coils is:

Consider two coils in which a current in one coil carrying $6$ $A$ causes the change in the flux in the second coil $12 \times 10^{-4}$ $Wb/turn$. The second coil has $2000$ turns. The mutual inductance between the coils is (in $H$)

Two coils $P$ and $Q$ have mutual inductance $M \text{ H}$. If the current in the coil $P$ is $I = I_0 \sin(\omega t)$, then the maximum value of e.m.f. induced in coil $Q$ is