b
(b ) \(\phi = BA\)\( = B \times \pi {r^2}\)

\(\therefore \phi \propto {r^2} \Rightarrow \phi = k{r^2}\)      ( \(k = constant\))

\(\therefore e = \frac{{d\phi }}{{dt}} = k.2r\frac{{dr}}{{dt}}\)

From \(0 -1\), \(r\) is constant,   \(\frac{{dr}}{{dt}} = 0\) hence, \(e = 0\)

From \(1 -2\), \(r = \alpha t,\)  \(\frac{{dr}}{{dt}} = \alpha \) hence \(e \propto r\)==> \(e \propto t\)

From \(2 -3\), again \(r\) is constant,   \(\frac{{dr}}{{dt}} = 0\) hence \(e = 0\)