A circular disc of radius 0.2 m is placed in a uniform magnetic field of induction $\frac{1}{\pi }$ $\left(\frac{Wb}{m^2}\right)$ in such a way that its axis makes an angle of ${60}^{°}$ with $\overrightarrow{B}$. The magnetic flux linked with the disc is 

(a) 0.02 Wb

(b) 0.06 Wb

(c) 0.08 Wb

(d) 0.01 Wb

A coil having number of turns \(N\) and cross-sectional area \(A\) is rotated in a uniform magnetic field \(B\) with an angular velocity \(\omega\). The maximum value of the emf induced in it is:
1. \(\frac{NBA}{\omega}\)
2. \(NBAω\)
3. \(\frac{NBA}{\omega^{2}}\)
4. \(NBAω^{2}\)

A current-carrying wire is placed below a coil in its plane, with current flowing as shown.

If the current increases –

1. no current will be induced in the coil 

2. an anticlockwise current will be induced in the coil 

3. a clockwise current will be induced in the coil 

4. the current induced in the coil will be first anticlockwise and then clockwise

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

When the current in a certain inductor coil is 5.0 A and is increasing at the rate of 10.0 A/s, the potential difference across the coil is 140V. When the current is 5.0 A and decreasing at the rate of 10.0 A/s, the potential difference is 60V. The self-inductance of the coil is –

1.  2H                 

2.  4H

3.  8H                 

4.  12H

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.  $850 \mathrm{\mu } \mathrm{V}$

The magnetic flux through a coil varies with time as $\mathrm{\varphi }= 5{\mathrm{t}}^2+6\mathrm{t}+9$. The ratio of emf at t = 3s to t = 0s will be 

1.  1 : 9                           

2.  1 : 6 

3.  6 : 1                           

4.  9 : 1

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.  $8\mathrm{L}$

PQ is an infinite current carrying conductor. AB and CD are smooth conducting rods on which a conductor EF moves with constant velocity v as shown. The force needed to maintain constant speed of EF is –

1. $\frac{1}{\mathrm{VR}}{\left[\frac{{\mathrm{\mu }}_{0}Iv}{2\mathrm{\pi }} \ln \left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^2$                       

2. $\frac{1}{\mathrm{VR}}{\left[\frac{{\mathrm{\mu }}_{0}Iv}{2} \ln \left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^2$

3. $\frac{\mathrm{V}}{\mathrm{R}}{\left[\frac{{\mathrm{\mu }}_0\mathrm{IV}}{2} \ln \left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^2$                         

4. $\frac{\mathrm{V}}{\mathrm{R}}{\left[\frac{{\mathrm{\mu }}_0\mathrm{IV}}{2\mathrm{\pi }} \ln \left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^2$