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 \(5.0\) 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.\(3.4 \times10^{-4} V\)