Motional EMF

Q. Magnetic moment of a square loop is M what will be the magnetic moment of the loop of its shape is changed to a circular

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. 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. 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. 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

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 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

Q. Two conducting rings $P$ and $Q$ of radii $r$ and $2r$ slide uniformly in opposite directions with centre of mass velocities $2v$ and $v$ respectively on a conducting surface $S$. There is an uniform magnetic field of magnitude $B$ perpendicular to the plane of the rings. The potential difference between the highest points of the two rings is

1. Zero
2. $4Bvr$
3. $8Bvr$
4. $16Bvr$

Q. A rod of length $10\text{cm}$ made up of conducting and non-conducting material (shaded part is non-conducting). The rod is rotated with constant angular velocity $10\text{rad/s}$ about point $O$, in constant magnetic field of $2T$ as shown in the figure. The induced emf between the point $A$ and $B$ of rod will be:

1. $0.029\text{V}$
2. $0.1\text{V}$
3. $0.051\text{V}$
4. $0.064\text{V}$

Q. Two rails of a railway track insulated from each other and the ground are connected to a milli voltmeter. What is the reading of voltmeter, when a train travels with a speed of 180 km/hr along the track. Given that the vertical component of earth's magnetic field is $0.2\times {10}^{-4}$ T and the rails are separated by 1 metre

1. ${10}^{-2}$ Volt
2. ${10}^{-4}$ Volt
3. ${10}^{-3}$ Volt
4. 1 Volt

Q. Swastick shown in figure is rotating at angular velocity of $\omega$ about O in a uniform magnetic field B perpendicular to the plane of the paper. Here, oa = oe = og = hg = ab = oc = cd = ef = L.

1. Potential difference between a and e is $2B\omega L^2$
2. Potential difference between a and c is $B\omega L^2$
3. Potential difference between b and e is $\frac{B\omega L^2}{2}$
   
4. Potential difference between e and g is zero

Q. This section contains 1 Matrix Match type question, which has 2 Columns (Column I and Column II). Column I has four entries (A), (B), (C) and (D), Column II has four entries (P), (Q), (R) and (S). Match the entries in Column I with the entries in Column II. Each entry in Column I may match with one or more entries in Column II.

इस खण्ड में 1 मैट्रिक्स मिलान प्रकार का प्रश्न है, जिसमें 2 कॉलम (कॉलम I तथा कॉलम II) हैं। कॉलम I में चार प्रविष्टियाँ (A), (B), (C) तथा (D) हैं, कॉलम II में चार प्रविष्टियाँ (P), (Q), (R) तथा (S) हैं। कॉलम I में दी गयी प्रविष्टियों का मिलान कॉलम II में दी गयी प्रविष्टियों के साथ कीजिए। कॉलम I में दी गयी प्रत्येक प्रविष्टि का मिलान कॉलम-II में दी गयी एक या अधिक प्रविष्टियों के साथ हो सकता है।

Match the Columns and choose the appropriate answer

कॉलमों का मिलान करें और सही उत्तर चुनें

A square metal wire frame is rotated with constant angular velocity ω about its end A inside an external uniform magnetic field B as shown. Match the entries of Column-I with the entries of Column-II.

एक वर्गाकार धात्विक तार फ्रेम को एक बाह्य एकसमान चुम्बकीय क्षेत्र B के अन्दर दर्शाए अनुसार अपने सिरे A के सापेक्ष नियत कोणीय वेग ω से घुमाया जाता है। कॉलम-I की प्रविष्टियों का मिलान कॉलम-II की प्रविष्टियों के साथ कीजिए।

	Column -I कॉलम-I		Column-II कॉलम-II
(A)	Induced emf between points A and C is बिन्दुओं A व C के मध्य प्रेरित वि.वा.ब. है	(P)	Bωa2
(B)	Induced emf between points A and B is बिन्दुओं A व B के मध्य प्रेरित वि.वा.ब. है	(Q)	$\frac{B\omega a^2}{2}$
(C)	Induced emf between points A and D is बिन्दुओं A व D के मध्य प्रेरित वि.वा.ब. है	(R)	2Bωa2
(D)	Induced emf between points B and D is बिन्दुओं B व D के मध्य प्रेरित वि.वा.ब. है	(S)	Zero शून्य

1. A-P, B-Q, C-Q, D-S
2. A-PQ, B-PQ, C-Q, D-S
3. A-PQR, B-Q, C-QR, D-RS
4. A-PQRS, B-PQ, C-PQ, D-RS

Q. A rod of mass m is released from rest in the vertical plane and slides along the rails. Find the terminal velocity of the rod if an B - field exists in the region as shown.

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

Q. A conducting rod of length $l$ falls vertically under gravity in a region of uniform magnetic field $B$. The field vectors are inclined at an angle $\theta$ with the horizontal as shown in figure. If the instantaneous velocity of the rod is $v$, the induced emf in the rod $ab$ is

1. $Blv$
2. $Blv\cos \theta$
3. $Blv\sin \theta$
4. $\text{Zero}$

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 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

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. 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 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. 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. Find velocity v(t) if the rod’s initial velocity was $v_0$ and mass is m.

1. $v=v_0$
2. $v=v_0\frac{B^2{l}^{2}v}{mR}t$
3. $v=v_0{e}^{-\left(\frac{B^2{l}^{2}t}{mR}\right)}$
4. $v=v_0+\frac{B^2{l}^{2}v}{mR}t$

Q.
A square metal wire loop of side 10 cm and resistance $1\Omega$ is moved with a constant velocity $v_0$ in a uniform magnetic field of induction B = 2 $weber/m^2$ as shown in the figure. The magnetic field lines are perpendicular to the plane of the loop (directed into the paper). The loop in connected to a network of resistors each of value $3\Omega$. The resistances of the lead wires OS and PQ are negligible. What should be the speed of the loop so as to have a steady current of 1 mA in the loop?

1. 0.02m/s
2. 2 m/s
3. 20 m/s
4. 200 m/s

Q. A pair of parallel conducting rails lie at right angle to a uniform magnetic field of 2.0 T as shown in the fig. Two resistors 10$\Omega$ and 5$\Omega$ are to slide without friction along the rail. The distance between the conducting rails is 0.1 m. Then

1. Induced current = $\frac{1}{150}A$ directed clockwise if 10$\Omega$ resistor is pulled to the right with speed $0.5m{s}^{-1}$ and 5$\Omega$ resistor is held fixed
2. Induced current = $\frac{1}{300}A$ directed anti-clockwise if 10$\Omega$ resistor is pulled to the right with speed $0.5m{s}^{-1}$ and 5$\Omega$ resistor is held fixed
3. Induced current = $\frac{1}{300}A$ directed clockwise if 5$\Omega$ resistor is pulled to the left at speed $0.5m{s}^{-1}$ and 10$\Omega$ resistor is held at rest
4. Induced current =$\frac{1}{150}A$ directed anti-clockwise if 5$\Omega$ resistor is pulled to the left with speed $0.5m{s}^{-1}$ and 10$\Omega$ resistor is held at rest

Q. Two conducting wires are joined together and are moving in a magnetic field perpendicular to the plane of the wires, as shown in the figure. If $V_P$ and $V_Q$ are the potentials at points $P$ and $Q$ respectively, then -

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

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 conductor of resistance $2\Omega$ and length 0.5m is moving with a uniform speed of 0.4 m/s perpendicular to a magnetic field of induction 1 T. If this is connected to a load resistance of $3\Omega$ , the current in the circuit is

1. 0.04 A
2. 0.02 A
3. 0.01 A
4. 0.08 A

Q. A and B are two identical rods of internal resistance $r=1\Omega .$ If $R=2\Omega ,V_A=4m/s,V_B=3m/s$, length of rods is 1 m, then current in R is (Magnetic field is 2T)

1. $1A$
2. $0.4A$
3. $0.6A$
4. $0.8A$

Q. The magnetic field $B$ shown in the figure is directed into the plane of the paper. $\text{ACDA}$ is a semicircular conducting loop of radius $r$ with the centre at $\text{O}$. The loop is now made to rotate clockwise with a constant angular velocity $\omega$ about an axis passing through $O$ and perpendicular to the plane of the paper. The resistance of the loop is $R$. Obtain an expression for the magnitude of the induced current in the loop.

1. $\frac{B\omega r^2}{R}$
2. $\frac{B\omega r^2}{4R}$
3. $\frac{B\omega r^2}{2R}$
4. $\frac{2B\omega r^2}{R}$