A long solenoid with \(15\) turns \(\text{cm}\) has a small loop of area \(2.0~\text {cm}^{2}\) placed inside the solenoid normal to its axis. If the current carried by the solenoid changes steadily from \(2.0~\text A\) to \(4.0~\text A\) in \(0.1~\text{s},\) what is the induced emf in the loop while the current is changing?
1. | \(7.5 \times 10^{-6}~ \text{V}\) | 2. | \(6.5 \times 10^{-6}~\text{V}\) |
3. | \(7.5 \times 10^{-5}~\text{V}\) | 4. | \(6.5 \times 10^{-5}~\text{V}\) |
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 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 The maximum emf induced in the coil is:
1. 0.603 V
2. 0.01 V
3. 0
4. 1 V
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 \(5.0~\text A\) to \(0~\text A\) in \(0.1~\text{s}\). If an average emf of \(200~\text V\) is induced, the self-inductance of the circuit is:
1. \(4~\text H\)
2. \(2~\text H\)
3. \(1~\text H\)
4. \(3~\text H\)
A rectangular wire loop of sides \(8~\text {cm}\) and \(2~\text{cm}\) with a small cut is moving out of a region of the uniform magnetic field of magnitude \(0.3~\text T\) directed normally to the loop. What is the EMF developed across the cut if the velocity of the loop is \(1~\text{cm/s}\) 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 \(1.5~\text H.\) If the current in one coil changes from \(0\) to \(20~\text A\) in \(0.5~\text s,\) what is the change of flux linkage with the other coil?
1. | \(35~\text{Wb}\) | 2. | \(25~\text{Wb}\) |
3. | \(30~\text{Wb}\) | 4. | \(20~\text{Wb}\) |
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 \(\lambda \) 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;
\(\vec B=B_0\hat k~~~~~~~(r\le a<R)\\ ~~~= 0~~~~~~~~~~~~(\text{otherwise}).\)
What is the angular velocity of the wheel after the field is suddenly switched off?
1. | \(-\dfrac{2 \pi B_0 a^2 \lambda}{M R} \hat{k}\) | 2. | \(-\dfrac{\pi B_0 a^2 \lambda}{M R} \hat{k}\) |
3. | \(-\dfrac{2 B_0 a^2 \lambda}{M R} \hat{k}\) | 4. | \(-\dfrac{2 B_0 a^2 \lambda}{\pi M R} \hat{k}\) |