$A$ conducting loop is placed in a uniform magnetic field with its plane perpendicular to the field. An $emf$ is induced in the loop if

$A$ highly conducting ring of radius $R$ is perpendicular to and concentric with the axis of a long solenoid as shown in the figure. The ring has a narrow gap of width $d$ in its circumference. The solenoid has a cross-sectional area $A$ and a uniform internal magnetic field of magnitude $B_0$. Starting at $t = 0$,the solenoid current is steadily increased such that the field magnitude at any time $t$ is given by $B(t) = B_0 + \alpha t$,where $\alpha > 0$. Assuming that no charge can flow across the gap,the end of the ring which has an excess of positive charge and the magnitude of the induced e.m.f. in the ring are respectively:

The diagram below shows two circular loops of wire ($A$ and $B$) centred on and perpendicular to the $X$-axis and oriented with their planes parallel to each other. The $Y$-axis passes vertically through loop $A$ (dashed line). There is a current $I_B$ in loop $B$ as shown in the diagram. Possible actions which we might perform on loop $A$ are:
$(I)$ move $A$ to the right along $X$-axis closer to $B$
$(II)$ move $A$ to the left along $X$-axis away from $B$
$(III)$ as viewed from above,rotate $A$ clockwise about $Y$-axis
$(IV)$ as viewed from above,rotate $A$ anti-clockwise about $Y$-axis
Which of the actions will induce a current in $A$ only in the direction shown?

$A$ rectangular coil of $20$ turns and an area of cross-section $25 \, cm^2$ has a resistance of $100 \, \Omega$. If a magnetic field which is perpendicular to the plane of the coil changes at the rate of $1000 \, T/s$,the current in the coil is $....... \, A$.

According to Faraday's law of electromagnetic induction:

As a result of a change in the magnetic flux linked to the closed loop as shown in the figure,an $e.m.f.$ $V$ volt is induced in the loop. The work done (in joule) in taking a charge $Q$ coulomb once along the loop is