$A$ square loop of side $2 \text{ cm}$ is placed in a time-varying magnetic field with magnitude $B = 0.4 \sin(300t) \text{ T}$. The normal to the plane of the loop makes an angle of $60^{\circ}$ with the field. The maximum induced emf produced in the loop is . . . . . . $\text{mV}$.

$A$ magnetic field given by $B(t) = (0.2t - 0.05t^2) \text{ T}$ is directed perpendicular to the plane of a circular coil containing $25$ turns of radius $1.8 \text{ cm}$ and whose total resistance is $5 \Omega$. The power dissipation at $3 \text{ s}$ is nearly: (in $\text{ } \mu\text{W}$)

If magnetic field passing through a coil of area $0.1 \ m^2$ is changing according to the equation $B = 20 \sin \left( \frac{2 \pi t}{3} \right) \text{ tesla}$,find the magnitude of induced emf at $t = 0.5 \ s$.

In the branch $AB$ of a circuit,as shown in the figure,a current $I = (t + 2) \ A$ is flowing,where $t$ is the time in seconds. At $t = 0$,the value of $(V_A - V_B)$ will be: (in $V$)

$A$ 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 $1.23 \times 10^{-8} \, \Omega m$).

$A$ conducting loop is placed in a time-varying magnetic field $B = \frac{\alpha}{t^2}$,where $\alpha$ is a positive constant. The magnetic field is directed into the plane of the loop. Determine the nature of the charge on plate $A$ of the capacitor $C$ connected in the loop.