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

$A$ 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:

$A$ 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

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....$mA$

$A$ rectangular wire loop of sides $8 \; cm$ and $2 \; cm$ with a small cut is moving out of a region of uniform magnetic field of magnitude $0.3 \; T$ directed normal to the loop. Suppose the loop is stationary but the current feeding the electromagnet that produces the magnetic field is gradually reduced so that the field decreases from its initial value of $0.3 \; T$ at the rate of $0.02 \; T \, s^{-1}$. If the cut is joined and the loop has a resistance of $1.6 \; \Omega$,how much power is dissipated by the loop as heat? What is the source of this power?

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 $, A$)?