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A coil has, 1,000 turns and 500 $c{m}^2$ 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$°$ in 0.2. The average e.m.f. induced in the coil, in milli-volts, is
1. 5
2. 10
3. 15
4. 20

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

An aluminum ring B faces an electromagnet A. The current I through A can be altered. Then :

 
(1) Whether I increases or decreases, B will not experience any force
(2) If I decrease, A will repel B
(3) If I increases, A will attract B
(4) If I increases, A will repel B

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

(1) P
(2) Q
(3) L
(4) M

A conducting square loop of side L and resistance R moves in its plane with a uniform velocity v perpendicular to one of its sides. A magnetic induction B constant in time and space, pointing perpendicular and into the plane of the loop exists everywhere. The current induced in the loop is:
    
1. $\frac{Blv}{R}$ clockwise
2. $\frac{Blv}{R}$ anticlockwise
3. $\frac{2Blv}{R}$ anticlockwise
4. Zero

A thin semicircular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic induction B. At the position MNQ, the speed of the ring is v and the potential difference developed across the ring is:
   

A uniform but time-varying magnetic field B(t) exists in a circular region of radius a and is directed into the plane of the paper, as shown. The magnitude of the induced electric field at point P at a distance r from the centre of the circular region 

(1) Is zero
(2) Decreases as $\frac{1}{r}$
(3) Increases as r
(4) Decreases as $\frac{1}{r^2}$

A conducting rod of length 2l is rotating with constant angular speed $\omega$ about its perpendicular bisector. A uniform magnetic field $\overrightarrow{B}$ exists parallel to the axis of rotation. The e.m.f. induced between two ends of the rod is 

(1) BΩl²
(2) $\frac{1}{2}B\omega l^2$
(3) $\frac{1}{8}B\omega l^2$
(4) Zero

A conducting wireframe is placed in a magnetic field that is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced current in wires AB and CD are:

Shown in the figure is a circular loop of radius r and resistance R. A variable magnetic field of induction B = B₀e^–t is established inside the coil. If the key (K) is closed, the electrical power developed right after closing the switch, at t=0, is equal to

(1) $\frac{B_0^2\pi r^2}{R}$
(2) $\frac{B_{0}10r^3}{R}$
(3) $\frac{B_0^2{\pi }^2{r}^{4}R}{5}$
(4) $\frac{B_0^2{\pi }^2{r}^4}{R}$

A rectangular loop with a sliding connector of length l = 1.0 m is situated in a uniform magnetic field B = 2 T perpendicular to the plane of the loop. Resistance of connector is r = 2 Ω. Two resistances of 6 Ω and 3 Ω are connected as shown in the figure. The external force required to keep the connector moving with a constant velocity v = 2 m/s is:

A conducting rod AC of length 4l is rotated about a point O in a uniform magnetic field $\overrightarrow{B}$ directed into the paper. AO = l and OC = 3l. Then

(1) $V_A-V_O=\frac{B\omega l^2}{2}$
(2) $V_O-V_C=\frac{7}{2}B\omega l^2$
(3) $V_A-V_C=4B\omega l^2$
(4) $V_C-V_O=\frac{9}{2}B\omega l^2$

A simple pendulum with bob of mass m and conducting wire of length L swings under gravity through an angle 2θ. The earth’s magnetic field component in the direction perpendicular to swing is B. Maximum potential difference induced across the pendulum is 

1. $2BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^{1/2}$
2. $BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$
3. $BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^{3/2}$
4. $BL\sin \left(\frac{{\displaystyle \theta }}{{\displaystyle 2}}\right){\left(gL\right)}^2$

Some magnetic flux is changed from a coil of resistance 10 ohm. As a result an induced current is developed in it, which varies with time as shown in figure. The magnitude of change in flux through the coil in webers is

(1) 2
(2) 4
(3) 6
(4) None of these

Figure (i) shows a conducting loop being pulled out of a magnetic field with a speed v. Which of the four plots shown in figure (ii) may represent the power delivered by the pulling agent as a function of the speed v

(1) a
(2) b
(3) c
(4) d

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

The back emf induced in a coil, when current changes from 1 ampere to zero in one milli-second, is 4 volts. The self-inductance of the coil is:
1. $1 H$                  
2. $4 H$
3. ${10}^{–3} H$              
4. $4$ $\times$ ${10}^{–3} H$

A wooden stick of length $3\mathcal{l}$ is rotated about an end with constant angular velocity $\mathrm{\omega }$ in a uniform magnetic field B perpendicular to the plane of motion. If the upper one third of its length is coated with copper, the potential difference across the whole length of the stick is –
   
1. $\frac{9\mathrm{B\omega }{\mathcal{l}}^2}{2}$                           
2. $\frac{4\mathrm{B\omega }{\mathcal{l}}^2}{2}$
3. $\frac{5\mathrm{B\omega }{\mathcal{l}}^2}{2}$                           
4. $\frac{\mathrm{B\omega }{\mathcal{l}}^2}{2}$

PQ is an infinite current carrying conductor. AB and CD are smooth conducting rods on which a conductor EF moves with constant velocity v as shown. The force needed to maintain constant speed of EF is –
                 
1. $\frac{1}{\mathrm{VR}}{\left[\frac{{\mathrm{\mu }}_{0}Iv}{2\mathrm{\pi }} \ln \left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^2$                       
2. $\frac{1}{\mathrm{VR}}{\left[\frac{{\mathrm{\mu }}_{0}Iv}{2} \ln \left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^2$
3. $\frac{\mathrm{V}}{\mathrm{R}}{\left[\frac{{\mathrm{\mu }}_0\mathrm{IV}}{2} \ln \left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^2$                         
4. $\frac{\mathrm{V}}{\mathrm{R}}{\left[\frac{{\mathrm{\mu }}_0\mathrm{IV}}{2\mathrm{\pi }} \ln \left(\frac{\mathrm{b}}{\mathrm{a}}\right)\right]}^2$

A circular ring of radius r is placed in a homogeneous magnetic field perpendicular to the plane of the ring. The field B changes with time according to the equation B = Kt, where K is a constant and t is the time. The electric field in the ring is
(1) $\frac{Kr}{4}$
(2) $\frac{Kr}{3}$
(3) $\frac{Kr}{2}$
(4) $\frac{K}{2r}$