$A$ conducting ring of radius $r$ is placed in a varying magnetic field perpendicular to the plane of the ring. If the rate at which the magnetic field varies is $x$,the electric field intensity at any point on the ring is:

$A$ long circular tube of length $10 \ m$ and radius $0.3 \ m$ carries a current $I$ along its curved surface as shown. $A$ wire-loop of resistance $0.005 \ \Omega$ and of radius $0.1 \ m$ is placed inside the tube with its axis coinciding with the axis of the tube. The current varies as $I = I_0 \cos(300t)$ where $I_0$ is constant. If the magnetic moment of the loop is $N \mu_0 I_0 \sin(300t)$,then $N$ is:

$A$ non-conducting ring (of mass $m$,radius $r$,having charge $Q$) is placed on a rough horizontal surface in a region with a transverse magnetic field. The magnetic field is increasing with time at a rate $R = dB/dt$. If the coefficient of friction between the surface and the ring is $\mu$,for the ring to remain in equilibrium,$\mu$ should be greater than:

$A$ uniform magnetic field $B$ exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of $4 \, mm$ and a total length of $30 \, cm$. The magnetic field changes with time at a steady rate $dB/dt = 0.032 \, T s^{-1}$. The induced current in the loop is close to $.... A$ (Resistivity of the metal wire is $1.23 \times 10^{-8} \, \Omega m$).

$A$ long straight solenoid with a cross-sectional radius $a$ and number of turns per unit length $n$ has a current varying with time as $I = I_0 \sin(\omega t)$ (or simply $dI/dt = I$). The magnitude of the electric field as a function of distance $r$ from the solenoid axis is,

$A$ solenoid of radius $R$ and length $L$ has a current $I = I_0 \sin \omega t$. The value of the induced electric field at a distance $r$ inside the solenoid is: