A long solenoid with \(15\) turns per cm has a small loop of area \(2.0\) cm² placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from \(2.0\) A to \(4.0\) A in \(0.1\) s, what is the induced emf in the loop while the current is changing?

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 centre and the ring is:
1. \(200~\text{V}\)
2. \(100~\text{V}\)
3. \(50~\text{V}\)
4. \(150~\text{V}\)

A circular coil of radius 8.0 cm and 20 turns is rotated about its vertical diameter with an angular speed of 50 rad/s in a uniform horizontal magnetic field of magnitude $3\times {10}^{-2} T.$ The maximum emf induced in the coil is:

1. 0.603 V
2. 0.01 V
3. 0
4. 1 V

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

A rectangular wire loop of sides \(8~\text {cm}\) and \(2~\text{cm}\) with a small cut is moving out of a region of the uniform magnetic field of magnitude \(0.3~\text T\) directed normally to the loop. What is the EMF developed across the cut if the velocity of the loop is \(1~\text{cm/s}\) in a direction normal to the longer side?
1. \(2.4 \times10^{-4}~\text V\)
2. \(2.0 \times10^{-3}~\text V\)
3. \(1.3 \times10^{-4}~\text V\)
4. \(1.7 \times10^{-3}~\text V\)

A pair of adjacent coils has a mutual inductance of \(1.5~\text H.\) If the current in one coil changes from \(0\) to \(20~\text A\) in \(0.5~\text s,\) what is the change of flux linkage with the other coil?
1. \(35~\text{Wb}\)
2. \(25~\text{Wb}\)
3. \(30~\text{Wb}\)
4. \(20~\text{Wb}\)

If a loop changes from an irregular shape to a circular shape, then magnetic flux linked with it:
1. decreases
2. remains constant
3. first decreases and then increases
4. increases

It is desired to measure the magnitude of the field between the poles of a powerful loudspeaker magnet. A small flat search coil of area $2 c{m}^2$ with 25 closely wound turns, is positioned normal to the field direction, and then quickly snatched out of the field region. Equivalently, one can give it a quick 90° turn to bring its plane parallel to the field direction). The total charge flown in the coil (measured by a ballistic galvanometer connected to the coil) is 7.5 mC. The combined resistance of the coil and the galvanometer is 0.50 $\Omega$. The field strength of the magnet is:

1. 0.55 T
2. 0.75 T
3. 0.67 T
4. 0.49 T