$A$ conducting ring is placed around the core of an electromagnet as shown in the figure. When key $K$ is pressed,the ring

In a coil of resistance $8 \, \Omega$,the magnetic flux due to an external magnetic field varies with time as $\phi = \frac{2}{3}(9 - t^2)$. The value of total heat produced in the coil,till the flux becomes zero,will be $.... \, J$.

$A$ bar magnet is allowed to fall vertically through a copper coil placed in a horizontal plane. The magnet falls with a net acceleration:

$A$ 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:

In a magnetic field of $0.05\,T$,the area of a coil changes from $101\,cm^2$ to $100\,cm^2$ without changing the resistance,which is $2\,\Omega$. The amount of charge that flows during this period is:

$A$ coil of $40 \ \Omega$ resistance has $100$ turns and a radius of $6 \ mm$. It is connected to an ammeter of resistance $160 \ \Omega$. The coil is placed perpendicular to a magnetic field. When the coil is taken out of the field,a charge of $32 \ \mu C$ flows through it. The intensity of the magnetic field is: (in $T$)