There are two long co-axial solenoids of the same length $l$. The inner and outer coils have radii $R_1$ and $R_2$ and a number of turns per unit length $n_1$ and $n_2$, respectively. The ratio of mutual inductance to the self-inductance of the inner-coil is:

The output of an AC generator is given by $E=E_m \sin \left(𝝎t-\frac{\mathrm{\pi }}{4}\right)$ and the current is given by $i=i_m \sin \left(𝝎t-\frac{3\mathrm{\pi }}{4}\right)$. The circuit contains a single element other than the generator. It is 

A thin wire is bent to form a square loop $ABCD.$ A battery of e.m.f $2 \mathrm{V}$ is connected between the points $A$ and $C.$ The magnetic induction due to the current in the loop at centre $O$ will