Motional EMF

Q. A conducting wire is moving towards right in a magnetic field B. The direction of induced current in the wire is shown in the figure. The direction of magnetic field will be

1. In the plane of paper pointing towards right
2. In the plane of paper pointing towards left
3. Perpendicular to the plane of paper and downwards
4. Perpendicular to the plane of paper and upwards

Q. Find the Flux through the rectangular piece of area $10\text{cm}\times 20\text{cm}$, when placed in a uniform electric field intensity of $200\text{N/C}$ as shown in figure.

1. $4{\text{Nm}}^2{\text{C}}^{-1}$
2. $3.5{\text{Nm}}^2{\text{C}}^{-1}$
3. $2.5{\text{Nm}}^2{\text{C}}^{-1}$
4. Zero

Q. A rectangular loop $ABCD$ is being pulled out of a magnetic field ${}^{\prime }{B}^{\prime }$ with uniform velocity ${}^{\prime }{v}^{\prime }$ by applying an external force $F$. Length $AB$ is $l$. Length $AD$ is $3l$ and total resistance of the loop is $R$. The thermal power developed in the loop and the force $F$ respectively is

1. $\frac{B^2{v}^2{l}^2}{R},\frac{B^2{l}^{2}v}{R}$
2. $\frac{9B^2{v}^2{l}^2}{R},\frac{9B^2{l}^{2}v}{R}$
3. $\frac{8B^2{v}^2{l}^2}{R},\frac{8B^2{l}^{2}v}{R}$
4. $\frac{3B^2{v}^2{l}^2}{R},\frac{3B^2{l}^{2}v}{R}$

Q. A rod of length 5 m is moving at a speed of 10m/s in a uniform magnetic field $\overrightarrow{B}=(3\hat{i}+4\hat{j}+2\hat{k})T$ as shown in figure. Potential difference across the length of the rod is

1. 0V
2. 2V
3. 100V
4. 25V

Q. A rectangular loop with a sliding connector of length $10\text{cm}$ is situated in uniform magnetic field perpendicular to plane of loop. The magnetic induction is $0.1$ Tesla and resistance of connector $\left(R\right)$ is $1$ ohm. The sides $AB$ and $CD$ have resistances $2$ ohm and $3$ ohm respectively. Find the current in the connector during its motion with constant velocity $1\text{m/s}$.

1. $\frac{1}{110}\text{A}$
2. $\frac{1}{220}\text{A}$
3. $\frac{1}{55}\text{A}$
4. $\frac{1}{440}\text{A}$

Q.

Find I, $i_1$, and $i_2$.

1. $3A,2A,1A$

2. $1A,\frac{2}{3}A,1A$

3. $1A,\frac{1}{3}A,\frac{2}{3}A$

4. $2A,\frac{4}{3}A,\frac{2}{3}A$

Q. A rod of length $l$ rotates with an uniform angular velocity $\omega$ about its perpendicular bisector. A uniform magnetic field $B$ exists parallel to the axis of rotation. The potential difference between the two ends of the rod is

1. Zero
2. $\frac{1}{2}\omega B{l}^2$
3. $B\omega l^2$
4. $2B\omega l^2$

Q. In a $p-n$ junction photo cell, the value of the photo electromotive force produced by monochromatic light is proportional to

Q. To induce an e.m.f. in a coil, the linking magnetic flux

1. Must decrease
2. Can either increase or decrease
3. Must remain constant
4. Must increase

Q. A wire cd of length l and mass m is sliding without friction on conducting rails ax and by as shown. The vertical rails are connected to each other with a resistance R between a and b. A uniform magnetic field B is applied perpendicular to the plane abcd such that cd moves with a constant velocity of

1. $\frac{mgR}{Bl}$
   
2. $\frac{mgR}{B^2{l}^2}$
   
3. $\frac{mgR}{B^3{l}^3}$
   
4. $\frac{mgR}{B^{2}l}$

Q. A conductor ABOCD moves along its bisector with a velocity of 1 m/s through a perpendicular magnetic field of 1 $wb/m^2$, as shown in fig. If all the four sides are of 1m length each, then the induced emf between points A and D is

1. \N
2. 1.41 volt
3. 0.71 volt ​
4. None of the above

Q. A moving-coil galvanometer has $100\text{turns}$ and each turn has an area $2.0{\text{cm}}^2$. The magnetic field produced by the magnet is $0.01\text{T}$. The deflection in the coil is $0.05\text{radian}$ when a current of $10\text{mA}$ is passed through it. Find the torsional constant of the suspension wire.

1. $4.0\times {10}^{-5}\text{Nm/rad}$
2. $1.0\times {10}^{-5}\text{Nm/rad}$
3. $2.0\times {10}^{-5}\text{Nm/rad}$
4. $3.0\times {10}^{-5}\text{Nm/rad}$

Q. A conducting rod of mass m and length l is given a velocity $V_0$ along the rails as shown is the figure. Magnetic field B exists perpendicular to the plane, then [Consider rails to be very long]

1. Time taken by rod to come to rest is $\frac{mR}{l^2{B}^2}$.
2. Distance travelled by rod before stopping is $\frac{m{v}_{0}R}{l^2{B}^2}$.
3. Heat generated across R till rod stops is $\frac{m{v}_0^2}{2}$.
4. Distance travelled by rod before stopping is infinite.

Q. Two parallel, conducting rails $1$ and $2$ are kept perpendicular to a uniform magnetic field $\left(B\right)$. The rails are at seperation $l$ and are joined at their ends by a resistance $R$. A conducting bar $AB$ is placed on the rails making ${60}^{\circ }$ with them. The bar is pulled with a velocity $v$ parallel to the rails. Find the current in the resistance $R$.

1. $\frac{\text{V}Bl}{R}$
2. $\frac{2B\text{V}l}{R}$
3. $\frac{B\text{V}l}{2R}$
4. $\frac{B\text{V}l}{4R}$

Q. A moving-coil galvanometer has $100\text{turns}$ and each turn has an area $2.0{\text{cm}}^2$. The magnetic field produced by the magnet is $0.01\text{T}$. The deflection in the coil is $0.05\text{radian}$ when a current of $10\text{mA}$ is passed through it. Find the torsional constant of the suspension wire.

1. $3.0\times {10}^{-5}\text{Nm/rad}$
2. $4.0\times {10}^{-5}\text{Nm/rad}$
3. $2.0\times {10}^{-5}\text{Nm/rad}$
4. $1.0\times {10}^{-5}\text{Nm/rad}$

Q. As shown in the figure a metal rod makes contact and complete the circuit. The circuit is perpendicular to the magnetic field with B=0.15 tesla If the resistance is $3\Omega$ , force needed to move the rod as indicated with a constant speed of 2m/sec is

1. $3.75\times {10}^{-3}N$
2. $3.75\times {10}^{-2}N$
3. $3.75\times {10}^{2}N$
4. $3.75\times {10}^{-4}N$

Q. Energy in a capacitor is independent of the manner in which the charge configuration of the capacitor is built up.

1. False
2. True

Q. A conducting rod of length L is moving in uniform magnetic field as shown in figure. Floor and wall are conducting with zero resistance. Resistance of rod is $R\Omega$ and its lower end is pulled with constant velocity v along x-axis. Rod remain in contact with wall and floor for full time with initially $\theta$ was ${90}^{\circ }$. So,

1. when $\theta ={30}^{\circ }$, current in the rod flows from B to A.
2. when $\theta ={30}^{\circ }$, current in the rod is $\frac{BVL}{2R}$
3. direction of current in the rod changes when $\theta ={30}^{\circ }$
4. potential difference across the rod measured by a voltmetre is zero.

Q. There is a uniform magnetic field $B$ directed in negative $z$ direction. A conductor $ABC$ has length $AB=l_1$, parallel to the $x-$axis, and length $BC=l_2$ parallel to the $y-$axis. $ABC$ moves in the $xy$ plane with velocity $v_x\hat{i}+v_y\hat{j}$. The potential difference between $A$ and $C$ is proportional to

1. $v_x{l}_1+v_y{l}_2$
2. $v_x{l}_2+v_y{l}_1$
3. $v_y{l}_1-v_x{l}_2$
4. $v_x{l}_1-v_y{l}_2$

Q. Find ${ϵ}_{ind}$ as a function of y.

1. $2yBv$
2. $2yBvsin\theta$
3. $yBv$
4. $2yBvtan\theta$

Q. In figure, the wires $P_1{Q}_1$ and $P_2{Q}_2$ are made to slide on the rails with the same speed of $5cm{s}^{-1}$. In this region, a magnetic field of $1T$ exists. The electric current in the $2\Omega$ resistance when both the wires are moving towards it is

1. $0.2mA$
2. $0.1mA$
3. $2mA$
4. Zero

Q. A conducting wire frame is placed in a magnetic field which 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

1. B to A and D to C
2. A to B and C to D
3. A to B and D to C
4. B to A and C to D
   

Q. A conductor ABOCD moves along its bisector with a velocity of 1 m/s through a perpendicular magnetic field of 1 $wb/m^2$, as shown in fig. If all the four sides are of 1m length each, then the induced emf between points A and D is

1. \N
2. 1.41 volt
3. 0.71 volt ​
4. None of the above

Q. An aeroplane in which the distance between the tips of the wings is 50m is flying horizontally with speed of 360 km/h over a place where the vertical component of earth’s magnetic field is $2\times {10}^4$ The potential difference between the tips of the wings would be

1. 0.1V
2. 1 V
3. 0.2V
4. 0.01V

Q. A conductor $ABOCD$ moves along its bisector with a velocity $1\text{m/s}$ through a perpendicular magnetic field of $1{\text{Wb/m}}^2$, as shown in figure. If all the four sides are of $1\text{m}$ length each, then the induced emf between A and D (in $\text{volts}$) is approximately (upto two decimals)

Q. A rectangular loop $ABCD$ is being pulled out of a magnetic field ${}^{\prime }{B}^{\prime }$ with uniform velocity ${}^{\prime }{v}^{\prime }$ by applying an external force $F$. Length $AB$ is $l$. Length $AD$ is $3l$ and total resistance of the loop is $R$. The thermal power developed in the loop and the force $F$ respectively is

1. $\frac{B^2{v}^2{l}^2}{R},\frac{B^2{l}^{2}v}{R}$
2. $\frac{9B^2{v}^2{l}^2}{R},\frac{9B^2{l}^{2}v}{R}$
3. $\frac{8B^2{v}^2{l}^2}{R},\frac{8B^2{l}^{2}v}{R}$
4. $\frac{3B^2{v}^2{l}^2}{R},\frac{3B^2{l}^{2}v}{R}$

Q.

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 loop. Resistance of connector is r = 2
$\Omega$. Two resistances of 6$\Omega$ and 3$\Omega$ are connected as shown in figure. The external force required to keep the connector moving with a constant velocity v = 2m/s is

1. 6N

2. 4N

3. 2N

4. 1N

Q. A metallic square loop ABCD is moving in its own plane with velocity v in a uniform magnetic field perpendicular to its plane as shown in the figure. An electric field is induced

1. In AD, but not in BC
2. In BC, but not in AD
3. Neither in AD nor in BC
4. In both AD and BC

Q. Find magnitude ${ϵ}_{ind}$ in positions A, B and C of the square frame of side l.

1. $Blv,0,Blv$
2. $0,0,0$
3. $Blv,Blv,Blv$
   
4. $0,Blv,0$

Q. A conducting rod PQ of length L = 1.0 m is moving with a uniform speed v = 2 m/s in a uniform magnetic field B=4.0 T directed into the paper. A capacitor of capacity $C=10\mu F$ is connected as shown in figure. Then

1. $qA=+80\mu CandqB=–80\mu C$
   
2. $qA=–80\mu CandqB=+80\mu C$
   
3. $qA=0=qB$
4. Charge stored in the capacitor increases exponentially with time