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 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

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

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 $25 c{m}^2,$ 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 ${10}^{-3} s.$ 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.)

1. 5.5 V

2. 4.5 V

3. 6.5 V

4. 4.0 V