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

Consider the following statements: 

A rod of length \(l\) rotates with uniform angular velocity \(\omega\) about an axis passing through its one end and perpendicular to its length. If a uniform magnetic field exists perpendicular to the axis of rotation, then induced emf across the two ends of the rod is :
1. \(\dfrac{1}{2}B\omega l^2\)
2. \(B\omega l^2\)
3. \(2B\omega l^2\)
4. zero