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.  $1.7<mspace\; width="1em"></mspace>\mathrm{V}$                             

2.  $85\sqrt{3}\times {10}^{-4}<mspace\; width="1em"></mspace>\mathrm{V}$

3.  $85\times {10}^{-4}<mspace\; width="1em"></mspace>\mathrm{V}$                 

4.  $850<mspace\; width="1em"></mspace>\mathrm{\mu }<mspace\; width="1em"></mspace>\mathrm{V}$

The magnetic flux through a coil varies with time as $\mathrm{\varphi }=<mspace\; width="1em"></mspace>5{\mathrm{t}}^2+6\mathrm{t}+9$. 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. $\frac{1}{\mathrm{VR}}{\left[\frac{{\mathrm{\mu }}_{0}Iv}{2\mathrm{\pi }}<mspace\; width="1em"></mspace>\ln <mspace\; width="1em"></mspace>\left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^2$                       

2. $\frac{1}{\mathrm{VR}}{\left[\frac{{\mathrm{\mu }}_{0}Iv}{2}<mspace\; width="1em"></mspace>\ln <mspace\; width="1em"></mspace>\left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^2$

3. $\frac{\mathrm{V}}{\mathrm{R}}{\left[\frac{{\mathrm{\mu }}_0\mathrm{IV}}{2}<mspace\; width="1em"></mspace>\ln <mspace\; width="1em"></mspace>\left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^2$                         

4. $\frac{\mathrm{V}}{\mathrm{R}}{\left[\frac{{\mathrm{\mu }}_0\mathrm{IV}}{2\mathrm{\pi }}<mspace\; width="1em"></mspace>\ln <mspace\; width="1em"></mspace>\left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^2$

A 50 turns circular coil has a radius of 3 cms, it is kept in a magnetic field acting normal to the area of the coil. The magnetic field B increased from 0.10 tesla to 0.35 tesla in 2 milliseconds. The average induced emf in the coil is-

1.  1.77 volts                     

2.  17.7 volts 

3.  177 volts                     

4.  0.177 volts

A semicircular wire of radius R is rotated with constant angular velocity $\mathrm{\omega }$ about an axis passing through one end and perpendicular to the plane of the wire.

There is a uniform magnetic field of strength B. The induced emf between the ends is?

1. ${\mathrm{B\omega R}}^2/2$                           

2. $2{\mathrm{B\omega R}}^2$

3. is variable                         

4. none of these

The inductance of a closed-packed coil of 400 turns is 8 mH. A current of 5 mA is passed through it. The magnetic flux through each turn of the coil is approximately-

1.  $0.1<mspace\; width="1em"></mspace>{\mathrm{\mu }}_0<mspace\; width="1em"></mspace>\mathrm{Wb}$                     

2.  $0.2<mspace\; width="1em"></mspace>{\mathrm{\mu }}_0<mspace\; width="1em"></mspace>\mathrm{Wb}$

3.  $1.0<mspace\; width="1em"></mspace>{\mathrm{\mu }}_0<mspace\; width="1em"></mspace>\mathrm{Wb}$                     

4.  $2.0<mspace\; width="1em"></mspace>{\mathrm{\mu }}_0<mspace\; width="1em"></mspace>\mathrm{Wb}$

The magnetic flux through each turn of a 100 turn coil is $\left({\mathrm{t}}^3<mspace\; width="1em"></mspace>–<mspace\; width="1em"></mspace>2\mathrm{t}\right)<mspace\; width="1em"></mspace>\times <mspace\; width="1em"></mspace>{10}^{-3}<mspace\; width="1em"></mspace>\mathrm{Wb}$, where t is in second. The induced emf at t = 2 s is

1. $-4<mspace\; width="1em"></mspace>\mathrm{V}$                       

2. $-1<mspace\; width="1em"></mspace>\mathrm{V}$

3. $+1<mspace\; width="1em"></mspace>\mathrm{V}$                       

4. $+4<mspace\; width="1em"></mspace>\mathrm{V}$

An emf of 15 volt is applied in a circuit containing 5 henry inductance and 10 ohm resistance. The ratio of the currents at time t = $\infty$ and at t = 1 second is -

1.  $\frac{{\mathrm{e}}^{1/2}}{{\mathrm{e}}^{1/2}-1}$                               

2.  $\frac{{\mathrm{e}}^2}{{\mathrm{e}}^2-1}$

3.  $1-{\mathrm{e}}^{-1}$                           

4.  ${\mathrm{e}}^{-1}$