A rod \(AB\) of length \(l\) is moving with constant speed \(v\) in a uniform magnetic field on a conducting \(U\)-shaped wire as shown. If the rate of loss of heat energy across resistance \(R\) is \(Q,\) then the force needed parallel to velocity to keep rod moving with constant speed \(v\) is:
1. \(Qv\)
2. \(\dfrac{Q}{v}\)
3. \(\dfrac{Q^2}{v}\)
4. \(Q^2v\)
A rectangular loop of wire shown below is coplanar with a long wire carrying current \(I.\)
The loop is pulled to the right as indicated. What are the directions of the induced current in the loop and the magnetic forces on the left and right sides of the loop?
Induced current | Force on left side | Force on right side | |
1. | counterclockwise | to the left | to the right |
2. | clockwise | to the left | to the right |
3. | counterclockwise | to the right | to the left |
4. | clockwise | to the right | to the left |
An electric potential difference will be induced between the ends of the conductor shown in the diagram when the conductor moves in the direction of:
1. \(P\)
2. \(Q\)
3. \(L\)
4. \(M\)
In a circuit with a coil of resistance \(2~\Omega\), the magnetic flux changes from \(2.0\) Wb to \(10.0\) Wb in \(0.2~\text{s}\). The charge that flows in the coil during this time is:
1. \(5.0~\text{C}\)
2. \(4.0~\text{C}\)
3. \(1.0~\text{C}\)
4. \(0.8~\text{C}\)
A long solenoid of diameter \(0.1\) m has \(2\times 10^{4}\) turns per meter. At the centre of the solenoid, a coil of \(100\) turns and a radius of \(0.01\) m is placed with its axis coinciding with the solenoid's axis. The current in the solenoid reduces at a constant rate from \(0\) A to \(4\) A in \(0.05\) s. If the resistance of the coil is \(10\pi^2~\Omega\), the total charge flowing through the coil during this time is:
1. | \(32\pi~\mu\text{C}\) | 2. | \(16~\mu\text{C}\) |
3. | \(32~\mu\text{C}\) | 4. | \(16\pi~\mu\text{C}\) |
A conducting square frame of side \(a\) and a long straight wire carrying current \(i\) are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity \(v\). The emf induced in the frame will be proportional to:
1. \(\frac{1}{x^2}\)
2. \(\frac{1}{(2x-a)^2}\)
3. \(\frac{1}{(2x+a)^2}\)
4. \(\frac{1}{(2x-a)\times (2x+a)}\)
In the figure shown a square loop \(PQRS\) of side \(a\) and resistance \(r\) is placed near an infinitely long wire carrying a constant current \(I\). The sides \(PQ\) and \(RS\) are parallel to the wire. The wire and the loop are in the same plane. The loop is rotated by \(180^{\circ}\) about an axis parallel to the long wire and passing through the midpoints of the side \(QR\) and \(PS.\) The total amount of charge which passes through any point of the loop during rotation is:
1. | \(\frac{\mu _{0}Ia}{2\pi r}~\mathrm{ln}(2)\) |
2. | \(\frac{\mu _{0}Ia}{\pi r}~\mathrm{ln}(2) \) |
3. | \(\frac{\mu _{0}Ia^2}{2\pi r}\) |
4. | cannot be found because the time of rotation not given. |
The number of turns in a coil of wire of fixed radius & length is \(600\) and its self-inductance is \(108\) mH. The self-inductance of a coil of \(500\) turns will be:
1. \(74\) mH
2. \(75\) mH
3. \(76\) mH
4. \(77\) mH
A magnetic rod is inside a coil of wire which is connected to an ammeter. If the rod is stationary, which of the following statements is true?
1. | The rod induces a small current. |
2. | The rod loses its magnetic field. |
3. | There is no induced current. |
4. | None of these. |