$A$ rectangular loop is being pulled at a constant speed $v$,through a region of certain thickness $d$,in which a uniform magnetic field $B$ is set up. The graph between position $x$ of the right-hand edge of the loop and the induced emf $E$ will be

$A$ coil of self-inductance $L$ is connected at one end of two rails as shown in the figure. $A$ connector of length $l$ and mass $m$ can slide freely over the two parallel rails. The entire setup is placed in a magnetic field of induction $B$ directed into the page. At an instant $t = 0$,an initial velocity $v_0$ is imparted to the connector,and as a result,it starts moving along the $x$-axis. Which of the following graphs best represents the displacement $x$ of the connector as a function of time $t$?

Two circular coils $P$ and $Q$ are fixed coaxially and carry currents $I_1$ and $I_2$ respectively.

Radio frequency choke uses a core of

$A$ small bar magnet of dipole moment $M$ is moving with speed $v$ along the $x$-direction towards a small closed circular conducting loop of radius $a$ with its centre $O$ at $x=0$ (see figure). Assume $x >> a$ and the coil has a resistance $R$. Which of the following statement$(s)$ is/are true?

$A$ rectangular loop of sides $12 \text{ cm}$ and $5 \text{ cm}$,with its sides parallel to the $x$-axis and $y$-axis respectively,moves with a velocity of $5 \text{ cm/s}$ in the positive $x$-axis direction in a space containing a variable magnetic field in the positive $z$-direction. The field has a gradient of $10^{-3} \text{ T/cm}$ along the negative $x$-direction and it is decreasing with time at the rate of $10^{-5} \text{ T/s}$. If the resistance of the loop is $6 \text{ m}\Omega$,the power dissipated by the loop as heat is . . . . . . $\times 10^{-9} \text{ W}$.