The figure shows a square loop \(L\) with a side length of \(5~\text{cm},\) which is connected to a network of resistances. The entire setup is moving to the right with a constant speed of \(1~\text{cm/s}.\) At a certain instant, a part of the loop \(L\) is in a uniform magnetic field of \(1~\text{T},\) perpendicular to the plane of the loop. If the resistance of the loop is \(1.7~\Omega,\) the current in the loop at that instant will be close to:

1. \(115~\mu \text{A}\)
2. \(150~\mu \text{A}\)
3. \(170~\mu \text{A}\)
4. \(60~\mu \text{A}\)

A circular coil of radius \(10\) cm is placed in a uniform magnetic field of \(3.0\times 10^{-5}~\mathrm{T}\) with its plane perpendicular to the field initially. It is rotated at constant angular speed about an axis along the diameter of coil and perpendicular to magnetic field so that it undergoes half of rotation in \(0.2\) s. The maximum value of EMF induced (in \(\mu V\)) in the coil will be close to:
1. \(5\)
2. \(10\)
3. \(15\)
4. \(20\)

An elliptical loop with resistance \(R,\) semi-major axis \(a,\) and semi-minor axis \(b\) is placed in a magnetic field as shown in the figure. If the loop is rotated about the \(x\text-\)axis with an angular frequency \(\omega,\) the average power loss in the loop due to Joule heating is:

                                
1. zero

2. \( \dfrac{\pi^2 {a}^2 {b}^2 {B}^2 \omega^2}{R} \)

3. \(\dfrac{\pi^2 {a}^2 {b}^2 {B}^2 \omega^2}{2 R} \)

4. \(\dfrac{\pi {abB}\omega}{R} \)

An infinitely long straight wire carrying current \(I\), one side opened rectangular loop and a conductor \(C\) with a sliding connector are located in the same plane, as shown in the figure. The connector has length \(l\) and resistance \(R\). It slides to the right with a velocity \(v\). The resistance of the conductor and the self inductance of the loop are negligible. The induced current in the loop, as a function of separation \(r\), between the connector and the straight wire is:

  
1. \( \frac{\mu_0}{\pi} \frac{I v l}{R r} \)
2. \( \frac{\mu_0}{2 \pi} \frac{I v l}{R r} \)
3. \(\frac{2 \mu_0}{\pi} \frac{I v l}{R r} \)
4. \( \frac{\mu_0}{4 \pi} \frac{I v l}{R r} \)