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:

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$\mathrm{\pi \; \mu C}$

A conducting square frame of side 'a' and a long straight wire carrying current i are located in the same plane as shown in the figure. The frame moves to the right with a constant velocity v. The emf induced in the frame will be proportional to:
      
1. 1/x²
2. 1/(2x-a)²
3. 1/(2x+a)²
4. 1/(2x-a) x (2x+a)