$A$ magnetic field given by $B(t) = (0.2t - 0.05t^2) \text{ T}$ is directed perpendicular to the plane of a circular coil containing $25$ turns of radius $1.8 \text{ cm}$ and whose total resistance is $5 \Omega$. The power dissipation at $3 \text{ s}$ is nearly: (in $\text{ } \mu\text{W}$)

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 $, A$)?

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....$mA$

$A$ uniform but time-varying magnetic field $B(t)$ exists in a circular region of radius $a$ and is directed into the plane of the paper,as shown. The magnitude of the induced electric field at point $P$ at a distance $r$ $(r > a)$ from the centre of the circular region is:

$A$ long solenoid of radius $R$ carries a time $(t)$-dependent current $I(t) = I_{0} t(1-t)$. $A$ ring of radius $2R$ is placed coaxially near its middle. During the time interval $0 \leq t \leq 1$,the induced current $(I_{R})$ and the induced $EMF$ $(V_{R})$ in the ring change as

$A$ uniform but time-varying magnetic field is present in a circular region of radius $R$. The magnetic field is perpendicular and into the plane of the loop and the magnitude of the field is increasing at a constant rate $\alpha$. There is a straight conducting rod of length $2R$ placed as shown in the figure. The magnitude of the induced emf across the rod is: