An electric potential difference will be induced between the ends of the conductor shown in the diagram when the conductor moves in the direction 

1. P

2. Q

3. L

4. M

Two rails of a railway track insulated from each other and the ground are connected to a milli voltmeter. What is the reading of voltmeter, when a train travels with a speed of \(180\) km/hr along the track.
(Given that the vertical component of earth's magnetic field is \(0.2\times 10^{-4}\) weber/m² and the rails are separated by \(1\) m) 
1. \(10^{-2}\) V
2. \(10^{-4}\) V
3. \(10^{-3}\) V
4. \(1\) V

A conducting square loop of side \(L\) and resistance \(R\) moves in its plane with a uniform velocity \(v\) perpendicular to one of its sides. A magnetic induction \(B\) constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere. The current induced in the loop is:

A conducting wire is moving towards right in a magnetic field B. The direction of induced current in the wire is shown in the figure. The direction of magnetic field will be 

1. In the plane of paper pointing towards right

2. In the plane of paper pointing towards left

3. Perpendicular to the plane of paper and down wards

4. Perpendicular to the plane of paper and upwards

One conducting U tube can slide inside another as shown in figure, maintaining electrical contacts between the tubes. The magnetic field B is perpendicular to the plane of the figure. If each tube moves towards the other at a constant speed v then the emf induced in the circuit in terms of B, l and v where l is the width of each tube, will be 

1. Zero

2. 2 Blv

3. Blv

4. – Blv

A copper rod of length l is rotated about one end perpendicular to the magnetic field B with constant angular velocity ω. The induced e.m.f. between the two ends is 

1. $\frac{1}{2}B\omega l^2$

2. $\frac{3}{4}B\omega l^2$

3. $B\omega l^2$

4. $2B\omega l^2$

A thin semicircular conducting ring of radius \(R\) is falling with its plane vertical in a horizontal magnetic induction \(B\). At the position \(MNQ\), the speed of the ring is \(v\) and the potential difference developed across the ring is:

Consider the situation shown in the figure. The wire AB is sliding on the fixed rails with a constant velocity. If the wire AB is replaced by semicircular wire, the magnitude of the induced current will 

1. Increase

2. Remain the same

3. Decrease

4. Increase or decrease depending on whether the semicircle bulges towards the resistance or away from it

A conducting rod of length 2l is rotating with constant angular speed $\omega$ about its perpendicular bisector. A uniform magnetic field $\overrightarrow{B}$ exists parallel to the axis of rotation. The e.m.f. induced between two ends of the rod is 

1. BΩl²

2. $\frac{1}{2}B\omega l^2$

3. $\frac{1}{8}B\omega l^2$

4. Zero

A square metallic wire loop of side \(0.1~\text m\) and resistance of \(1~\Omega\) is moved with a constant velocity in a magnetic field of \(2~\text{wb/m}^2\) as shown in the figure. The magnetic field is perpendicular to the plane of the loop and the loop is connected to a network of resistances. What should be the velocity of the loop so as to have a steady current of \(1~\text{mA}\) in the loop?

           
1. \(1~\text{cm/s}\)
2. \(2~\text{cm/s}\)
3. \(3~\text{cm/s}\)
4. \(4~\text{cm/s}\)