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

$A$ 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 $t = \frac{3\pi}{2\omega}$.

Flux $\phi$ (in weber) in a closed circuit of resistance $10 \, \Omega$ varies with time $t$ (in $s$) according to the equation $\phi = 6t^2 - 5t + 1$. What is the magnitude of the induced current at $t = 0.25 \, s$ (in $, A$)?

$A$ 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,

One turn of insulated wire in the form of a planar square frame with side $l = 0.2\,m$ and resistance $1\,\Omega$ is placed in a uniform magnetic field perpendicular to the plane of the frame. The current passing through the turn when the magnetic field starts to decrease at a constant rate of $0.1\,T/s$ is....$mA$

$A$ 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?