A long solenoid with $15$ turns $\text{cm}$ has a small loop of area $2.0~\text {cm}^{2}$ placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from $2.0~\text A$ to $4.0~\text A$ in $0.1~\text{s},$ 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?

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