$A$ magnetic field of $2 \times 10^{-2} \,T$ acts at right angles to a coil of area $100 \,cm^2$ with $50$ turns. The average e.m.f. induced in the coil is $0.1 \,V$, when it is removed from the field in time $t$. The value of $t$ is (in seconds): (in $s$)

The magnetic flux linked with a coil is given by the equation $\phi$ (in webers) = $8t^2 + 3t + 5$. The induced $e.m.f.$ in the coil at the $4^{th}$ second will be.......$units$.

$A$ line charge ($\lambda$ per unit length) is in the form of a circular wheel of radius $a$ and moment of inertia $I$,initially at rest. It is free to rotate in a horizontal plane. There is a coaxial magnetic field $B = B_0 \hat{k}$ extending up to a radius $b$ $(b < a)$. If the magnetic field is switched off,the angular velocity $\omega$ of the wheel is given by:

$A$ coil of $40 \ \Omega$ resistance has $100$ turns and a radius of $6 \ mm$. It is connected to an ammeter of resistance $160 \ \Omega$. The coil is placed perpendicular to a magnetic field. When the coil is taken out of the field,a charge of $32 \ \mu C$ flows through it. The intensity of the magnetic field is: (in $T$)

$A$ current-carrying solenoid is approaching a conducting loop as shown in the figure. The direction of the induced current as observed by an observer on the other side of the loop will be

Magnetic flux linked with the coil is given by $\phi(t) = 2t^2 + 2t + 1$ and its resistance is $10 \ \Omega$. The current passing through the coil at $t = 2 \ s$ is . . . . . . $A$.