$A$ 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.

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 $t = 0.5 \ s$.

$A$ circular region of radius $R$ has a uniform magnetic field $B = B_0 + B_0 t(-\hat{k})$. At $t = 0$,what is the acceleration of a charged particle of mass $m$ and charge $q$ placed at a distance $r$ $(r > R)$ from the center?

$A$ square loop of side $2.0\,cm$ is placed inside a long solenoid that has $50$ turns per centimetre and carries a sinusoidally varying current of amplitude $2.5\,A$ and angular frequency $700\,rad\,s^{-1}$. The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is $x \times 10^{-4}\,V$. The value of $x$ is $.........$ (Take $\pi = \frac{22}{7}$)

$A$ coil is placed in a time-varying magnetic field. The power dissipated due to current induced in the coil is $P_1$. If the number of turns is doubled and the radius of the wire is halved,the power dissipated is $P_2$. Then $P_1: P_2$ is

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