a
Magnetic flux ( \(\phi\) ) through ring is \(\phi=\pi(R)^{2} . B\)

\(\phi=\left(\pi \mathrm{R}^{2}\right)\left(\mu_{0} \mathrm{n} \mathrm{I}\right)=\left(\pi \mathrm{R}^{2} \mu_{0} \mathrm{n} \mathrm{I}_{0}\right)\left(\mathrm{t}-\mathrm{t}^{2}\right)\)

Induced e.m.f. of \(\mathrm{V}_{\mathrm{R}}=\frac{-\mathrm{d} \phi}{\mathrm{dt}}\)

\(=\left(\pi \mathrm{R}^{2} \mu_{0} \mathrm{nI}_{0}\right)(2 \mathrm{t}-1)\)

and induced current \(\mathrm{I}_{\mathrm{R}}=\frac{\pi \mathrm{R}^{2} \mu_{0} \mathrm{nI}_{0}(2 \mathrm{t}-1)}{\mathrm{R}_{\mathrm{R}}}\)

\(\left(\mathrm{R}_{\mathrm{R}} \rightarrow \text { Resistance of Ring }\right)\)

Clearly \(\mathrm{V}_{\mathrm{R}}\) and \(\mathrm{I}_{\mathrm{R}}\) are zero at \(\mathrm{t}=\frac{1}{2}=0.5 \mathrm{sec}\)

and their sign also changes at \(t=0.5\) sec.