A solenoid of length $L$, radius $R$, and $N$ turns carries a current $I$. A small circular loop of radius $r$ (where $r\ll R$) is placed at the center of the solenoid with its plane perpendicular to the axis. If the current in the solenoid is reversed in time $t$, what is the average induced EMF in the small loop?

1. A.$\frac{2{\mu }_{0}NI\pi r^2}{Lt}$
2. B.$\frac{{\mu }_{0}NI\pi r^2}{Lt}$
3. C.$\frac{4{\mu }_{0}NI\pi r^2}{Lt}$
4. D.$\frac{{\mu }_{0}NI\pi r^2}{2Lt}$