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

1.		2.
3.		4.

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 1 of radius R is outside the region of magnetic field as shown in the figure. Then, the emf generated is

(1) zero in loop1 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) $\frac{dB}{dt}{\mathrm{\pi r}}^2 \mathrm{in} loop 1 and zero \mathrm{in} \mathrm{loop} 2$

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 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 with the disc is 

(a) 0.02 Wb

(b) 0.06 Wb

(c) 0.08 Wb

(d) 0.01 Wb

A coil having number of turns \(N\) and cross-sectional area \(A\) is rotated in a uniform magnetic field \(B\) with an angular velocity \(\omega\). The maximum value of the emf induced in it is:
1. \(\frac{NBA}{\omega}\)
2. \(NBAω\)
3. \(\frac{NBA}{\omega^{2}}\)
4. \(NBAω^{2}\)