$($a$)(10$ marks$)$ Figure $1$ shows the magnetic field with the direction out of the page. If the magnetic flux through the loop increases according to the relation ${}_B=6\mathrm{.}0t^2+7\mathrm{.}0tmT{m}^2,$ with $t$ in unit of second. What is the magnitude of the emf induced in the loop when $t=2s?$ Is the direction of the current through the resistor $R$ to the right or left?

$($b$)(10$ mark$)$ A small loop of area $6\mathrm{.}8m{m}^2$ is placed inside a long solenoid that has $854$ turns $\frac{?}{cm}$ and carries a sinusoidally varying current of amplitude $1\mathrm{.}28$ A with angular frequency $212ra\frac{d}{s}.$ The central axes of the loop and the solenoid coincide. What is the amplitude of the emf induced in the loop?