$A$ square loop of side $10 \ cm$ and resistance $0.7 \ \Omega$ is placed vertically in the east-west plane. $A$ uniform magnetic field of $0.20 \ T$ is set up across the plane in the north-east direction. The magnetic field is decreased to zero in $1 \ s$ at a steady rate. Then,the magnitude of the induced emf is $\sqrt{x} \times 10^{-3} \ V$. The value of $x$ is . . . . . . .

An aluminium ring $B$ faces an electromagnet $A$. The current $I$ through $A$ can be altered. Which of the following statements is correct?

Lenz's law gives

$A$ 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:

Out of the following,which law obeys the law of conservation of energy?

Consider a magnet surrounded by a wire loop with an on/off switch $S$ as shown in the figure. If the switch is thrown from the off position (open circuit) to the on position (closed circuit), will a current flow in the circuit? Explain.