At time $t=0$, a magnetic field of $1000 \; \text{Gauss}$ is passing perpendicularly through the area defined by the closed loop shown in the figure. If the magnetic field reduces linearly to $500 \; \text{Gauss}$ in the next $5 \; \text{s}$, then the induced $EMF$ in the loop is ........ $\mu \text{V}$.

The figure shows a uniform magnetic field $B$ confined to a cylindrical volume,which is increasing at a constant rate. The instantaneous acceleration experienced by an electron placed at point $P$ is:

$A$ uniform magnetic field of induction $B$ is confined to a cylindrical region of radius $R$. The magnetic field is increasing at a constant rate of $\frac{dB}{dt} \ (T/s)$. An electron is placed at the point $P$ on the periphery of the field. The acceleration experienced by the electron is:

$A$ circular loop of radius $20 \text{ cm}$ and resistance $2 \text{ } \Omega$ is placed in a time-varying magnetic field $\vec{B} = (2t^2 + 2t + 3) \text{ T}$. The plane of the loop is perpendicular to the magnetic field. The induced current in the loop at $t = 3 \text{ s}$ is $\frac{\alpha}{50} \text{ A}$. The value of $\alpha$ is . . . . . . .

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 $V$)

$A$ conducting circular loop made of a thin wire has an area of $3.5 \times 10^{-3} \, m^2$ and a resistance of $10 \, \Omega$. It is placed perpendicular to a time-dependent magnetic field $B(t) = (0.4 \, T) \sin(50 \pi t)$. The field is uniform in space. The net charge flowing through the loop during the interval $t = 0 \, s$ to $t = 10 \, ms$ is close to.......$\mu C$.