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?

1.\(7.5 \times 10^{-6}\ V\)
2.\(6.5 \times 10^{-6}\ V\)
3.\(7.5 \times 10^{-5}\ V\)
4.\(6.5 \times 10^{-5}\ V\)

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. \(150~\text{V}\)

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

A horizontal straight wire 10 m long extending from east to west is falling with a speed of 5.0 ms^-1 at right angle to the horizontal component of the earth's magnetic field, \(0.30 \times 10^{-4} \mathrm{~Wb} \mathrm{~m}^{-2}\)$\mathrm{}$
. The instantaneous value of the emf induced in the wire is:

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

A rectangular wire loop of sides \(8\) cm and \(2\) cm with a small cut is moving out of a region of the uniform magnetic field of magnitude \(0.3\) T directed normal to the loop. What is the EMF developed across the cut if the velocity of the loop is \(1\) 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 H. If the current in one coil changes from 0 to 20 A in 0.5 s, what is the change of flux linkage with the other coil?

1. 35 Wb

2. 25 Wb

3. 30 Wb

4. 20 Wb

A jet plane is traveling towards the west at a speed of 1800 km/h. What is the voltage difference developed between the ends of the wing having a span of 25 m, if the Earth’s magnetic field at the location has a magnitude of 5 × 10^–4 T and the dip angle is 30°.

1.2.712 V
2.3.125 V
3.1.112 V
4.3.011V

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