$A$ square loop of side $5 \ cm$ enters a magnetic field with a velocity of $1 \ cm/s$. The front edge enters the magnetic field at $t = 0$. Which graph best depicts the induced $emf$?

The bob of a simple pendulum is replaced by a magnet. The oscillations are set along the length of the magnet. $A$ copper coil is added so that one pole of the magnet passes in and out of the coil. The coil is short-circuited. Then which one of the following happens?

$A$ 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 $t=\left(\frac{1}{K}\right) \ln \left(\frac{3}{2}\right)$.

Two similar circular loops carry equal currents in the same direction. On moving the coils further apart,the electric current will

The network shown in the figure is part of a complete circuit. If at a certain instant the current $i$ is $5 \, A$ and is decreasing at the rate of $10^3 \, A/s$, then $V_B - V_A$ is: (in $ \, V$)

$A$ circular coil of $500$ turns of wire has an enclosed area of $0.1\,m^2$ per turn. It is kept perpendicular to a magnetic field of induction $0.2\,T$ and rotated by $180^o$ about a diameter perpendicular to the field in $0.1\,s$. How much charge will pass when the coil is connected to a galvanometer with a combined resistance of $50\,\Omega$?