$A$ coil is placed in a time-varying magnetic field. If the number of turns in the coil were to be halved and the radius of the wire doubled,the electrical power dissipated due to the current induced in the coil would be: (Assume the coil to be short-circuited.)

$A$ conducting loop having a capacitor is moving outward from the magnetic field. Which plate of the capacitor will be positive?

$A$ square loop of side $12 \; cm$ with its sides parallel to $X$ and $Y$ axes is moved with a velocity of $8 \; cm \, s^{-1}$ in the positive $x$-direction in an environment containing a magnetic field in the positive $z$-direction. The field is neither uniform in space nor constant in time. It has a gradient of $10^{-3} \; T \, cm^{-1}$ along the negative $x$-direction (that is, it increases by $10^{-3} \; T \, cm^{-1}$ as one moves in the negative $x$-direction), and it is decreasing in time at the rate of $10^{-3} \; T \, s^{-1}$. Determine the direction and magnitude of the induced current in the loop if its resistance is $4.50 \; m\Omega$.

$A$ part of a complete circuit is shown in the figure. At some instant,the value of current $I$ is $1\, A$ and it is decreasing at a rate of $10^{2}\, A s^{-1}$. The value of the potential difference $V_{P} - V_{Q}$ (in volts) at that instant is:

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$)

Two long parallel wires whose centres are at a distance $d$ apart carry equal currents in opposite directions. If the flux within the wires is neglected,the inductance of such an arrangement of wire of length $l$ and radius $a$ will be