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, \(0.30 \times 10^{-4} ~\text{Wb m}^{-2}\). The instantaneous value of the emf induced in the wire is:

1.	\(2.5 \times 10^{-3} ~\text V\)	2.	\(1.5 \times 10^{-4} ~\text V\)
3.	\(2.5 \times 10^{-4}~\text V\)	4.	\(1.5 \times 10^{-3} ~\text V\)

Current in a circuit falls from \(5.0\) A to \(0\) A in \(0.1~\text{s}\). 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?

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

A line charge λ per unit length is lodged uniformly onto the rim of a wheel of mass M and radius R. The wheel has light non-conducting spokes and is free to rotate without friction about its axis (as shown in the figure). A uniform magnetic field extends over a circular region within the rim. It is given by,

$\overrightarrow{B}=B_0 \hat{k} \left(r\le a; a<R\right)$
$= 0 \left(otherwise\right)$

What is the angular velocity of the wheel after the field is suddenly switched off?

1. \(-\frac{2 \pi B_0 a^2 \lambda}{M R} \hat{k}\)
2. \(-\frac{\pi B_0 a^2 \lambda}{M R} \hat{k}\)
3. \(-\frac{2 B_0 a^2 \lambda}{M R} \hat{k}\)
4. \(-\frac{2 B_0 a^2 \lambda}{\pi M R} \hat{k}\)

A straight wire carries a current of 50 A and the loop is moved to the right with a constant velocity, v= 10 m/s. the induced emf in the loop at the instant when x = 0.2 m, is:
(Take a = 0.1 m and assume that the loop has a large resistance.)
 

1.\(3.4 \times10^{-5} V\)
2.\(1.7 \times10^{-5} V\)
3.\(1.7 \times10^{-4} V\)
4.\(3.4 \times10^{-4} V\)
 

An air-cored solenoid having a length of \(30\) cm whose area is \(25   \text{ cm}^{2} ,\) and the number of turns is \(500\) carries a current of \(2.5\) A. Suddenly the current is turned off and the time taken for it is \(10^{- 3}  \text{ s} .\) What would be the average value of the induced back-emf across the ends of the open switch in the circuit? (Neglect the variation in the magnetic field near the ends of the solenoid.)

Figure shows a metal rod PQ resting on the smooth rails AB and positioned between the poles of a permanent magnet. The rails, the rod, and the magnetic field are in three mutually perpendicular directions. A galvanometer G connects the rails through a switch K. Length of the rod = 15 cm, B = 0.50 T, resistance of the closed-loop containing the rod = 9.0 mΩ. Assume the field to be uniform.

What is the magnitude of the induced emf if we will keep the K open and the rod is moved with the speed of 12 cm/s in the direction shown in the figure?

1. 9.8 mV
2. 4.9 mV
3. 0.9 mV
4. 9.0 mV