Figure shows a uniform magnetic field $B$ confined to a cylindrical volume and increasing at a constant rate. The instantaneous acceleration experienced by an electron placed at $P$ 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 radius $R$ and mass $m$ having charge $q$ uniformly distributed over its circumference is placed on a rough horizontal surface. $A$ vertical time-varying uniform magnetic field $B = 4t^2$ is switched on at time $t=0$. The coefficient of friction between the ring and the table,if the ring starts rotating at $t = 2 \, s$,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 $V$)

$A$ magnetic field in a certain region is given by $\vec B = B_0 \cos(\omega t) \hat k$. $A$ coil of radius $a$ with resistance $R$ is placed in the $xy$-plane with its centre at the origin in the magnetic field (see figure). Find the magnitude and the direction of the current at $(a, 0, 0)$ at $t = \frac{\pi}{2\omega}$,$t = \frac{\pi}{\omega}$,and $t = \frac{3\pi}{2\omega}$.

$A$ 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 . . . . . . $\text{mV}$.