A long solenoid of diameter 0.1m has 2$\times {10}^4$ turns per meter. At the centre of the solenoid, a coil of 100 turns and radius 0.01m is placed with its axis coinciding with the solenoid's axis.  The current in the solenoid reduces at a constant rate to 0 A from 4A in 0.05s. If the resistance of the coil is $10{\pi }^2\Omega$, 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 uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate $\frac{dB}{dt}$. Loop 2 of radius R is outside the region of magnetic field as shown in the figure. Then the emf generated is-

(1) zero in loop 1 and zero in loop 2

(2) $-\frac{dB}{dt}{\mathrm{\pi r}}^2$ $\mathrm{in}$ $\mathrm{loop}$ $1$ $\mathrm{and}-\frac{\mathrm{dB}}{\mathrm{dt}}{\mathrm{\pi r}}^2$ $\mathrm{in}$ $\mathrm{loop}$ $2$

(3) $-\frac{dB}{dt}{\mathrm{\pi r}}^2$ $\mathrm{in}$ $loop$ $1$ $and$ $zero$ $\mathrm{in}$ $\mathrm{loop}$ $2$

(4) $\frac{2dB}{dt}{\mathrm{\pi r}}^2$ $\mathrm{in}$ $loop$ $1$ $and$ $zero$ $\mathrm{in}$ $\mathrm{loop}$ $2$

An electron moves on a straight-line path XY as shown. The abcd is a coil adjacent to the path of the electron. What will be the direction of the current, if any induced in the coil?
            

A wire loop is rotated in a magnetic field. The frequency of change of direction of the induced emf is

(1) once per revolution

(2) twice per revolution

(3) four times per revolution

(4) six times per revolution

A coil of resistance 400$\Omega$ is placed in a magnetic field. If the magnetic flux $\varphi \left(Wb\right)$ linked with the coil varies with time t (sec) as $\varphi =50t^2+4.$

The current in the coil at t=2s is 

(1) 0.5A                                           

(2) 0.1A

(3) 2A                                               

(4) 1A

A conducting circular loop is placed in a uniform magnetic field $0.04 T$ with its plane perpendicular to the magnetic field. The radius of the loop starts shrinking at $2 \mathrm{mm}/\mathrm{s}.$ The induced emf in the loop when the radius is 2 cm is

1. $3.2 \mathrm{\pi \mu V}$                                      2. $4.8 \mathrm{\pi \mu V}$

3. $0.8 \mathrm{\pi \mu V}$                                      4. $1.6 \mathrm{\pi \mu V}$

A rectangular, a square, a circular and an elliptical loop, all in the (x-y) plane, are moving out of a uniform magnetic field with a constant velocity, $\overrightarrow{\mathbf{v}}=\mathrm{v}\hat{\mathbf{i}}.$ The magnetic field is directed along the negative z-axis direction. The induced emf, during the passage of these loops, out of the field region, will not remain constant for 

(1) the rectangular, circular and elliptical loops

(2) the circular and the elliptical loops

(3) only the elliptical loop

(4) any of the four loops

a long solenoid has 500 turns. When a current of 2 A is passed through it, the resulting magnetic flux linked with each turn of the solenoid is $4\times {10}^{-3}$ Wh.  The self-inductance of the solenoid is 

(a) 2.5 h

(b) 2.0 H 

(c) 1.0 H

(d) 4.0 H

A circular disc of radius 0.2 m is placed in a uniform magnetic field of induction $\frac{1}{\pi }$ $\left(\frac{Wb}{m^2}\right)$ in such a way that its axis makes an angle of ${60}^{°}$ with $\overrightarrow{B}$. The magnetic flux linked to the disc will be:
1. 0.02 Wb
2. 0.06 Wb
3. 0.08 Wb
4. 0.01 Wb

If induction of magnetic field at a point is B and energy density is U, then which of the following graphs is correct?

1. 

2. 

3. 
4.