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

A thin semicircular conducting ring (PQR) of radius r is falling with its plane vertical in a horizontal magnetic field B,as shown in figure. The potential difference developed across the ring when its speed is v,is


(1) zero

(2) Bvπr²/2 and P is at higher potential

(3) πrBv and R is at higher potential  

(4) 2rBv and R is at higher potential

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 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 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 

1. 2.5 h

2. 2.0 H 

3. 1.0 H

4. 4.0 H

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

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 square loop of side 5 cm enters a magnetic field with 1 cms^-1. The front edge enters the magnetic field at t = 0 then which graph best depicts emf

1. 

2. 

3. 

4.

The current i in an induction coil varies with time t according to the graph shown in figure. Which of the following graphs shows the induced emf (e) in the coil with time

1.              2.
3.               4. 

A flexible wire bent in the form of a circle is placed in a uniform magnetic field perpendicular to the plane of the coil. The radius of the coil changes as shown in the figure. The graph of induced emf in the coil is represented by

1.

2.

3.

4.