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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 \(2~\Omega,\) the magnetic flux changes from \(2.0\) Wb to \(10.0\) Wb in \(0.2\) s. The charge that flows in the coil during this time is:
1. \(5~\text{C}\)
2. \(4~\text{C}\)
3. \(1~\text{C}\)
4. \(0.8~\text{C}\)

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:
                 

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 \(B = 2T\) perpendicular to the plane of the loop. Resistance of connector is \(r=2~\Omega\). Two resistances of \(6~\Omega\) and \(3~\Omega\) 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:
       
1. \(6~\text{N}\)
2. \(4~\text{N}\)
3. \(2~\text{N}\)
4. \(1~\text{N}\)

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. \(1~\text{H}\)
2. \(4~\text{H}\)
3. \(10^{-3}~\text{H}\)
4. \(4\times10^{-3}~\text{H}\)

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) $\frac{K}{2r}$