The radius of the circular conducting loop shown in the figure is $R.$ The magnetic field is decreasing at a constant rate $\alpha.$ The resistance per unit length of the loop is $r.$ Find the current in the wire $AB,$ where $AB$ is one of the diameters.

$A$ metallic ring of radius $a$ and resistance $R$ is held fixed with its axis along a spatially uniform magnetic field whose magnitude is $B = B_0 \sin \omega t$. Gravity is neglected. Then,

$A$ charged particle of charge $q$ and mass $m$ is placed at a distance $2R$ from the centre of a vertical cylindrical region of radius $R$ where the magnetic field varies as $\vec{B} = (4t^2 - 2t + 6) \hat{k}$, where $t$ is time. Then which of the following statement$(s)$ is/are true?

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 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:

$A$ 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.......$\mu C$.