An emf can be induced in a stationary coil if it is kept in

$A$ line charge $\lambda$ per unit length is lodged uniformly onto the rim of a wheel of mass $M$ and radius $R$. The wheel has light non-conducting spokes and is free to rotate without friction about its axis. $A$ uniform magnetic field extends over a circular region within the rim. It is given by,
$B = -B_{0} \hat{k}$ for $r \leq a$ (where $a < R$)
$B = 0$ otherwise.
What is the angular velocity of the wheel after the field is suddenly switched off?

The circular wire in the figure below encircles a solenoid in which the magnetic flux is increasing at a constant rate out of the plane of the page. The clockwise emf around the circular loop is $\varepsilon_{0}$. By definition,a voltmeter measures the voltage difference between two points given by $V_{b}-V_{a}=-\int_{a}^{b} E \cdot ds$. We assume that $a$ and $b$ are infinitesimally close to each other. The values of $V_{b}-V_{a}$ along path $1$ and $V_{a}-V_{b}$ along path $2$,respectively,are

$A$ 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.......$mC$.

$A$ conducting ring of radius $r$ is placed perpendicularly inside a time-varying magnetic field given by $B = B_0 + \alpha t$ as shown in the figure. $B_0$ and $\alpha$ are positive constants. Find the $emf$ produced in the ring.

$A$ non-conducting ring (of mass $m$,radius $r$,having charge $Q$) is placed on a rough horizontal surface in a region with a transverse magnetic field. The magnetic field is increasing with time at a rate $R = dB/dt$. If the coefficient of friction between the surface and the ring is $\mu$,for the ring to remain in equilibrium,$\mu$ should be greater than: