The current in a coil varies with time t as $\mathrm{I}$ $=$ $3{\mathrm{t}}^2+$ $2\mathrm{t}$. If the inductance of coil be 10 mH, the value of induced e.m.f. at \(t=2~\mathrm{s}\) will be:
1. \(0.14~\mathrm{V}\)
2. \(0.12~\mathrm{V}\)
3. \(0.11~\mathrm{V}\)
4. \(0.13~\mathrm{V}\)

A coil of a mean area of 500 $c{m}^2$ and 1000 turns is held perpendicular to a uniform field of 0.4 Gauss. The coil is turned through $180°$ in $\frac{1}{10}$ seconds. The average induced e.m.f. is:

The network shown in figure is a part of a complete circuit. If at a certain instant, the current 'i' is 10 A and is increasing at the rate of $4\times {10}^3$ A/sec, then $V_A-V_B$ is:

A coil having an area $A_0$ is placed in a magnetic field which changes from $B_0$ $to$ $4B_0$ in time interval t. The average EMF induced in the coil will be:

1. $\frac{3A_0{B}_0}{t}$

2. $\frac{4A_0{B}_0}{t}$

3. $\frac{3B_0}{A_{0}t}$

4. $\frac{4B_0}{A_{0}t}$

A rod AB of length l is moving with constant speed v in a uniform magnetic field on a conducting U-shaped wire as shown. If the rate of loss of heat energy across resistance R is Q, then the force needed parallel to velocity to keep rod moving with constant speed v is:

1.  Qv

2.  $\frac{\mathrm{Q}}{\mathrm{v}}$

3.  $\frac{{\mathrm{Q}}^2}{\mathrm{v}}$

4.  ${\mathrm{Q}}^2\mathrm{v}$

A coil has 1,000 turns and 500 ${\mathrm{cm}}^2$ as its area. The plane of the coil is placed at right angles to a magnetic field of $2\times {10}^{-5}$ $Wb/m^2$. The coil is rotated through  \(180^{0}\)$$  in 0.2 seconds. The average e.m.f. induced in the coil, in milli-volts, is:

A rectangular loop of wire shown below is coplanar with a long wire carrying current \(I.\)
               
The loop is pulled to the right as indicated. What are the directions of the induced current in the loop and the magnetic forces on the left and right sides of the loop?

An electric potential difference will be induced between the ends of the conductor shown in the diagram when the conductor moves in the direction of:

1. P
2. Q
3. L
4. M

In a circuit with a coil of resistance 2 ohms, the magnetic flux changes from 2.0 Wb to 10.0 Wb in 0.2 second. The charge that flows in the coil during this time is:
1. 5.0 coulomb
2. 4.0 coulomb
3. 1.0 coulomb
4. 0.8 coulomb

A long solenoid of diameter 0.1 m has 2$\times {10}^4$ turns per meter. At the centre of the solenoid, a coil of 100 turns and a radius of 0.01 m is placed with its axis coinciding with the solenoid's axis.  The current in the solenoid reduces at a constant rate from 0 A to 4 A in 0.05 s. If the resistance of the coil is $10{\pi }^{\mathrm{2 }}\Omega$, the total charge flowing through the coil during this time is:

1. 32$\mathrm{\pi \; \mu C}$

2. 16 $\mu C$

3. 32 $\mu C$

4. 16$\mathrm{\pi \; \mu C}$