On what factor does the induced current depend?

$A$ long straight wire is parallel to one edge of a rectangular loop as shown in the figure. If the current in the long wire varies with time as $I = I_0 e^{-t/\tau}$,what will be the induced $emf$ in the loop?

$A$ conducting ring of radius $a$ is rotated about a point $O$ on its periphery as shown in the figure in a plane perpendicular to a uniform magnetic field $B$ which exists everywhere. The rotational velocity is $\omega$. Choose the correct statement$(s)$ related to the induced current in the ring.

Two different coils have self-inductance $L_1 = 8 \, mH$ and $L_2 = 2 \, mH$. The current in both coils is increased at the same constant rate. At a certain instant of time,the power supplied to the two coils is the same. At that time,the current,induced voltage,and energy stored in the first coil are $i_1, V_1$,and $W_1$ respectively. Corresponding values for the second coil at the same instant are $i_2, V_2$,and $W_2$ respectively. Then:

$A$ conducting square loop of side $L$,mass $M$ and resistance $R$ is moving in the $XY$ plane with its edges parallel to the $X$ and $Y$ axes. The region $y \geq 0$ has a uniform magnetic field,$\vec{B}=B_0 \hat{k}$. The magnetic field is zero everywhere else. At time $t=0$,the loop starts to enter the magnetic field with an initial velocity $v_0 \hat{\imath} \text{ m/s}$,as shown in the figure. Considering the quantity $K=\frac{B_0^2 L^2}{RM}$ in appropriate units,ignoring self-inductance of the loop and gravity,which of the following statements is/are correct:
$(A)$ If $v_0=1.5 KL$,the loop will stop before it enters completely inside the region of magnetic field.
$(B)$ When the complete loop is inside the region of magnetic field,the net force acting on the loop is zero.
$(C)$ If $v_0=\frac{KL}{10}$,the loop comes to rest at $t=\left(\frac{1}{K}\right) \ln \left(\frac{5}{2}\right)$.
$(D)$ If $v_0=3 KL$,the complete loop enters inside the region of magnetic field at time $t=\left(\frac{1}{K}\right) \ln \left(\frac{3}{2}\right)$.

The current $I$ through a coil varies with time $t$ as shown in the graph. Plot the graph for the induced $emf$ $e$ versus time $t$ for the coil.