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.  $0.1 {\mathrm{\mu }}_0 \mathrm{Wb}$                     

2.  $0.2 {\mathrm{\mu }}_0 \mathrm{Wb}$

3.  $1.0 {\mathrm{\mu }}_0 \mathrm{Wb}$                     

4.  $2.0 {\mathrm{\mu }}_0 \mathrm{Wb}$

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

1. $-4 \mathrm{V}$                       

2. $-1 \mathrm{V}$

3. $+1 \mathrm{V}$                       

4. $+4 \mathrm{V}$

A copper rod of length 0.19 m is moving parallel to a long wire with a uniform velocity of 10 m/s. The long wire carries 5 ampere current and is perpendicular to the rod. The ends of the rod are at distances 0.01 m and 0.2 m from the wire. The emf induced in the rod will be-

1.  $10 \mathrm{\mu V}$                           

2.  $20 \mathrm{\mu V}$

3.  $30 \mathrm{\mu V}$                           

4.  $40 \mathrm{\mu V}$

Rate of increment of energy in an inductor with time in series LR circuit getting charge with battery of emf E is best represented by – [inductor has initially zero current]

1.                        

2. 

3.                        

4. 

A long solenoid having 1000 turns per cm is carrying alternating current of one ampere peak value. A search coil of area of cross-section $1\times {10}^{-4} {\mathrm{m}}^2$ and of 20 turns is placed in the middle of the solenoid so that its plane is perpendicular to the axis of the solenoid. The search coil registers a peak voltage $2.5\times {10}^{-2} \mathrm{V}$. The frequency of the current in the solenoid is -

1.  1.6 per second                   

2.  0.16 per second

3.  15.9 per second                 

4.  15.85 per second

A coil of the area $7 {\mathrm{cm}}^2$ and of 50 turns is kept with its plane normal to a magnetic field B. A resistance of 30 ohms is connected to the resistance-less coil. B is $75{\mathrm{e}}^{-200\mathrm{t}}$ Gauss. The current passing through the resistance at t = 5 ms will be-

1.  $0.64 \mathrm{mA}$                     

2.  $1.05 \mathrm{mA}$ 

3.  $1.75 \mathrm{mA}$                     

4.  $2.60 \mathrm{mA}$

Assertion: When a coil is joined to a cell, the current through the cell will be 10% less than its steady-state value at time $\mathrm{t} =\mathrm{\tau } {\log }_{\mathrm{e}} 10$, where $\mathrm{\tau }$ is the time constant of the circuit.

Reason: When a coil is joined to a cell, the growth of current is given by $\mathrm{i}={\mathrm{i}}_0{\mathrm{e}}^{-\mathrm{t}/\mathrm{\tau }}$