A metal rod moves at a constant velocity in a direction perpendicular to its length. A constant, uniform magnetic field exists in space in a direction perpendicular to the rod as well as its velocity. Select the correct statement (s) from the following : 

1. The entire rod is at the same electric potential 

2. There is an electric field in the rod 

3. The electric potential is highest at the center of the rod and decreases towards its ends 

4. The electric potential is lowest at the center of the rod and increases towards its ends.

The mutual inductance of a pair of coils is 2H. If the current  of the coil changes from 10A to zero in 0.1s, the emf induced in the other coil is – 

1.  2 V                     

2.  20 V 

3.  0.2 V                 

4.  200 V

A current-carrying wire is placed below a coil in its plane, with current flowing as shown in the figure. If the current increases,:

The back emf induced in a coil, when current changes from \(1\) ampere to zero in one milli-second, is \(4\) volts. The self-inductance of the coil is:
1. \(1~\text{H}\)
2. \(4~\text{H}\)
3. \(10^{-3}~\text{H}\)
4. \(4\times10^{-3}~\text{H}\)

Average energy stored in a pure inductance L when a current i flows through it, is

1.  ${\mathrm{Li}}^2$                           

2.  $2{\mathrm{Li}}^2$

3.  ${\mathrm{Li}}^2/4$                       

4.  ${\mathrm{Li}}^2/2$

A small magnet is along the axis of a coil and its distance from the coil is 80 cm. In this position the flux linked with the coil are $4 \times {10}^{–5}$ weber turns. If the coil is displaced 40 cm towards the magnet in 0.08 second, then the induced emf produced in the coil will be -

1.  0.5 mV                       

2.  1 mV 

3.  7 mV                           

4.  3.5 mV

A wooden stick of length $3\mathcal{l}$ is rotated about an end with constant angular velocity $\mathrm{\omega }$ in a uniform magnetic field B perpendicular to the plane of motion. If the upper one third of its length is coated with copper, the potential difference across the whole length of the stick is –

1. $\frac{9\mathrm{B\omega }{\mathcal{l}}^2}{2}$                           

2. $\frac{4\mathrm{B\omega }{\mathcal{l}}^2}{2}$

3. $\frac{5\mathrm{B\omega }{\mathcal{l}}^2}{2}$                           

4. $\frac{\mathrm{B\omega }{\mathcal{l}}^2}{2}$

A train is moving at a rate of 72 km/hr on a horizontal plane. If the earth's horizontal component of magnetic field is 0.345 A/m and the angle of dip is 30°, then the potential difference across the two ends of a compartment of length 1.7 m will be-

1.  $1.7 \mathrm{V}$                             

2.  $85\sqrt{3}\times {10}^{-4} \mathrm{V}$

3.  $85\times {10}^{-4} \mathrm{V}$                 

4.  $850 \mathrm{\mu } \mathrm{V}$

An air-plane with 20m wing spread is flying at $250 {\mathrm{ms}}^{-1}$ straight south parallel to the earth’s surface. The earth’s magnetic field has a horizontal component of $2 \times {10}^{–5}$ $\mathrm{Wb} {\mathrm{m}}^{–2}$ and the dip angle is 60º. Calculate the induced emf between the plane tips is:

1.  0.174 V                 

2.  0.173 V 

3.  1.173 V                 

4.  0.163 V

A wire of fixed lengths is wound on a solenoid of length $\mathcal{l}$ and radius r. Its self inductance is found to be L. Now if same wire is wound on a solenoid of length $\mathcal{l}/2$ and radius r/2, then the self inductance will be –

1.  $2\mathrm{L}$                     

2.  $\mathrm{L}$ 

3.  $4\mathrm{L}$                     

4.  $8\mathrm{L}$