A big circular coil with $1000$ turns and an average radius of $10 \text{ m}$ is rotating about its horizontal diameter at a rate of $2 \text{ rad s}^{-1}$. The vertical component of the Earth's magnetic field at that location is $2 \times 10^{-5} \text{ T}$, and the electrical resistance of the coil is $12.56 \Omega$. The maximum induced current in the coil will be:

A conducting circular loop of face area $2.5 \times 10^{-3} \text{ m}^2$ is placed perpendicular to a magnetic field which varies as $B=0.5 \sin(100\pi t) \text{ T}$. The magnitude of induced EMF at time $t=0 \text{ s}$ is:

A coil of resistance $400\Omega$ is placed in a magnetic field. If the magnetic flux $\phi\;(\text{Wb})$ linked with the coil varies with time $t\;(\text{sec})$ as $\phi=50t^2+4$. The current in the coil at $t=2\text{s}$ is:

A wooden stick of length $3l$ is rotated about an end with constant angular velocity $\omega$ in a uniform magnetic field $B$ perpendicular to the plane of motion. If the upper one third of its length is coated with copper, the potential difference across the whole length of the stick is:

The primary and secondary coils of a transformer have 50 and 1500 turns respectively. If the magnetic flux $\phi$ linked with the primary coil is given by $\phi = \phi_0 + 4t$, where $\phi$ is in Weber, $t$ is time in seconds, and $\phi_0$ is a constant, the output voltage across the secondary coil is:

In which of the following devices, the eddy current effect is not used?

The current in an inductor of self-inductance $4 \text{ H}$ changes from $4 \text{ A}$ to $2 \text{ A}$ in $1 \text{ s}$. The emf induced in the coil is:

In the above diagram, a strong bar magnet is moving towards solenoid-2 from solenoid-1. The direction of induced current in solenoid-1 and that in solenoid-2, respectively, are through the directions:

A rod of length $L$ rotates with a small uniform angular velocity $\omega$ about its perpendicular bisector. A uniform magnetic field $B$ exists parallel to the axis of rotation. The potential difference between the centre of the rod and an end is: