A superconducting loop of radius R has self inductance L. A uniform and constant magnetic field B is applied perpendicular to the plane of the loop. Initially current in this loop is zero. The loop is rotated by 180°. The current in the loop after rotation is equal to –

1. zero                                 

2. $\frac{{\mathrm{B\pi R}}^2}{\mathrm{L}}$

3. $\frac{2{\mathrm{B\pi R}}^2}{\mathrm{L}}$                           

4. $\frac{{\mathrm{B\pi R}}^2}{2\mathrm{L}}$

A coil of inductance 8.4 mH and resistance 6$\mathrm{\Omega }$ is connected to a 12 V battery. The current in the coil is 1.0 A at approximately the time. 

1.  500 ms                 

2.  20 ms 

3.  35 ms                   

4.  1 ms

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

Loop A of radius (r << R) moves towards loop B with a constant velocity v in such a way that their planes are always parallel.

What is the distance (x) between the two loops when the induced emf in loop A is maximum –

1. $\mathrm{R}$                                     

2. $\frac{\mathrm{R}}{\sqrt{2}}$

3. $\frac{\mathrm{R}}{2}$                                     

4. $\mathrm{R}\left(1-\frac{1}{\sqrt{2}}\right)$

The current in an L – R circuit builds up to ${\left(3/4\right)}^{\mathrm{th}}$ of its steady state value in 4 seconds. The time constant of this circuit is?

1. $\frac{1}{\ln <mspace\; width="1em"></mspace>2}\sec$                       

2. $\frac{2}{\ln <mspace\; width="1em"></mspace>2}\sec$

3. $\frac{3}{\ln <mspace\; width="1em"></mspace>2}\sec$                       

4. $\frac{4}{\ln <mspace\; width="1em"></mspace>2}\sec$

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.  ${\mathrm{e}}^{-1}$

A circular coil of radius 5 cm has 500 turns of a wire. The approximate value of the coefficient of self induction of the coil will be -

1.  $25<mspace\; width="1em"></mspace>\mathrm{mH}$                           

2.  $25\times {10}^{-3}<mspace\; width="1em"></mspace>\mathrm{mH}$

3.  $50\times {10}^{-3}<mspace\; width="1em"></mspace>\mathrm{mH}$               

4.  $50\times {10}^{-3}<mspace\; width="1em"></mspace>\mathrm{H}$