The figure shows a uniform magnetic field $B$ confined to a cylindrical volume,which is increasing at a constant rate. The instantaneous acceleration experienced by an electron placed at point $P$ is:

$A$ short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved, the electric power dissipated would be .............

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 $, A$)?

$A$ 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?

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 loop of radius $20 \text{ cm}$ and resistance $2 \text{ } \Omega$ is placed in a time-varying magnetic field $\vec{B} = (2t^2 + 2t + 3) \text{ T}$. The plane of the loop is perpendicular to the magnetic field. The induced current in the loop at $t = 3 \text{ s}$ is $\frac{\alpha}{50} \text{ A}$. The value of $\alpha$ is . . . . . . .