a
\(\text { Here, } \phi=50 t^{2}+4\, \mathrm{Wb}, R=400\, \Omega\)

Induced \(emf\), \(\varepsilon=-\frac{d \phi}{d t}=-\frac{d}{d t}\left(50 t^{2}+4\right)=-100 t \,\mathrm{V}\)

At \(t=2 \,\mathrm{s}, \varepsilon=-200\, \mathrm{V}\)

\(|\varepsilon|=200\, \mathrm{V}\)

Induced current in the coil at \(t=2\, \mathrm{s}\) is

\(I=\frac{|\varepsilon|}{R}=\frac{200\, \mathrm{V}}{400\, \Omega}=\frac{1}{2}\, \mathrm{A}=0.5\, \mathrm{A}\)