According to Faraday's Law of Induction, the magnitude of the induced electromotive force ($|\varepsilon|$) is equal to the rate of change of magnetic flux ($\phi$) .

1. Calculate Induced EMF ($|\varepsilon|$): $|\varepsilon| = \left| \frac{d\phi}{dt} \right|$ Given $\phi = 50t^2 + 4$, differentiating with respect to time $t$: $\frac{d\phi}{dt} = \frac{d}{dt}(50t^2 + 4) = 100t$ At $t = 2\text{s}$: $|\varepsilon| = 100(2) = 200 \text{ V}$

2. Calculate Induced Current ($I$): Using Ohm's Law ($I = \frac{V}{R}$), where $V = |\varepsilon|$ and $R$ is the resistance : $I = \frac{|\varepsilon|}{R} = \frac{200 \text{ V}}{400 \Omega}$ $I = 0.5 \text{ A}$