A copper rod of mass \(m\) slides under gravity on two smooth parallel rails \(l\) distance apart and set at an angle \(\theta\) to the horizontal as shown in fig. At the bottom, the rails are joined by a resistance \(R\). There is a uniform magnetic field perpendicular to the plane of the rails. The terminal velocity of the rod is:

                          

 

1. \(\frac{m g R \cos \theta}{B^{2} l^{2}}\)

2. \(\frac{m g R \sin \theta}{B^{2} l^{2}}\)

3. \(\frac{m g R \tan \theta}{B^{2} l^{2}}\)

4. \(\frac{m g R \cot \theta}{B^{2} l^{2}}\) 

A square coil \(ACDE\) with its plane vertical is released from rest in a horizontal uniform magnetic field \(\vec {B}\) of length \(2L\) (figure). The acceleration of the coil is:

Two coils of \(10\) turns each are arranged such that the mutual inductance between them is \(150\) mH. The magnetic flux linked through one coil when \(2\) amperes current will flow in another coil, will be:
1. \(1\times 10^{-3}~\text{Wb}\)
2. \(10\times 10^{-3}~\text{Wb}\)
3. \(20\times 10^{-3}~\text{Wb}\)
4. \(30\times 10^{-3}~\text{Wb}\)

A \(10\) H inductor carries a current of \(20\) A. How much ice at \(0^{\circ}\text{C}\) could be melted by the energy stored in the magnetic field of the inductor?
Latent heat of ice is  \(2.26\times 10^{3}\)${\mathrm{}}^{}$ J/kg .

Some magnetic flux is changed from a coil of resistance \(10~\Omega\)$\mathrm{}$. As a result, an induced current is developed in it, which varies with time as shown in the figure. The magnitude of change in flux through the coil in Wb is:

When the current in the portion of the circuit shown in the figure is \(2\) A and increases at the rate of \(1\) A/s, the measured potential difference \(V_{ab}=8\) V. However, when the current is \(2\) A and decreases at the rate of \(1\) A/s, the measured potential difference \(V_{ab}= 4\) V. The value of \(R\) and \(L\) is:

In the circuit diagram shown in figure, \(R = 10~\Omega\), \(L = 5~\text{H},\) \(E = 20~\text{V}\) and \(i = 2~\text{A}\). This current is decreasing at a rate of \(1.0\) A/s. \(V_{ab}\) at this instant will be:

A straight solenoid has \(50\) turns per cm in primary coil and \(200\) turns in the secondary coil. The area of cross-section of the solenoid is \(4\) cm². Calculate the mutual inductance.
1. \(5.0~\text{H}\)
2. \(5.0\times 10^{-4}~\text{H}\)
3. \(2.5~\text{H}\)
4. \(2.5\times 10^{-4}~\text{H}\)

A \(1~\text{m}\) long metallic rod is rotating with an angular frequency of \(400~\text{rad/s}\)$$ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field of \(0.5~\text{T}\) parallel to the axis exists everywhere. The emf induced between the center and the ring is:
1. \(200~\text{V}\)
2. \(100~\text{V}\)
3. \(50~\text{V}\)
4. \(150~\text{V}\)

Current in a circuit falls from \(5.0\) A to \(0\) A in \(0.1\) s. If an average emf of \(200\) V is induced, the self-inductance of the circuit is:
1. \(4\) H
2. \(2\) H
3. \(1\) H
4. \(3\) H