The figure shows a circular area of tthe radius $R$ where a uniform magnetic field $\overrightarrow{B}$ is going into the plane of the paper and increasing in magnitude at a constant rate. In that case, which of the following graphs, drawn schematically, correctly shows the variation of the induced electric field $E\left(r\right)$?

A metallic rod of length $l$ is tied to a string of length $2l$ and made to rotate with angular speed $\omega$ on a horizontal table with one end of the string fixed. If there is a vertical magnetic field B in the region, the e.m.f. induced across the ends of the rod is:

As shown in the figure an inductor of inductance $200 \mathrm{mH}$ is connected to an $\mathrm{AC}$ source of emf $220 \mathrm{V}$and frequency $50 \mathrm{Hz}$. The instantaneous voltage of the source is $0 \mathrm{V}$ when the peak value of current is $\frac{\sqrt{a}}{\pi } \mathrm{A}$. The value of $a$ is _____ .