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 \(5\times 10^{-4}~\text{T}\) and the dip angle is \(30^{\circ}\).
1. \(2.712~\text{V}\)
2. \(3.125~\text{V}\)
3. \(1.112~\text{V}\)
4. \(3.011~\text{V}\)

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

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 emf induced in the moving rod if the direction of the magnetic field is changed from perpendicular to parallel to the rails?

1. 0
2. 9 mV
3. 0.9 mV
4. None of these

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

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. \(1.7 \times10^{-3}~\text V\)