A wooden stick of length $3\mathcal{l}$ is rotated about an end with constant angular velocity $\mathrm{\omega }$ 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 –

1. $\frac{9\mathrm{B\omega }{\mathcal{l}}^2}{2}$                           

2. $\frac{4\mathrm{B\omega }{\mathcal{l}}^2}{2}$

3. $\frac{5\mathrm{B\omega }{\mathcal{l}}^2}{2}$                           

4. $\frac{\mathrm{B\omega }{\mathcal{l}}^2}{2}$

The resistance in the following circuit is increased at a particular instant. At this instant the value of resistance is \(10~\Omega.\) The current in the circuit will be:

A circular loop of radius R carrying current I lies in the x-y plane with its centre at the origin. The total magnetic flux through the x-y plane is 

1. Directly proportional to I

2. Directly proportional to R

3. Directly proportional to R²

4. Zero

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

A long solenoid of diameter \(0.1\) m has \(2 \times 10^4\) turns per meter. At the center of the solenoid, a coil of \(100\) turns and radius \(0.01\) m is placed with its axis coinciding with the solenoid axis. The current in the solenoid reduces at a constant rate to \(0\) A from \(4\) A in \(0.05\) s. If the resistance of the coil is \(10\pi^2~\Omega\), then the total charge flowing through the coil during this time is:
1. \(16~\mu \text{C}\)
2. \(32~\mu \text{C}\)
3. \(16\pi~\mu \text{C}\)
4. \(32\pi~\mu \text{C}\)