Motional EMF

Practice Questions:

Question 1: moderate

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

1. \[V_{A}-V_{0}=\frac{B\omega l^{2}}{2}\]

2. \[V_{0}-V_{C}=\frac{7}{2}B\omega l^{2}\]

3. \[V_{A}-V_{C}=4 B\omega l^{2}\]

4. \[V_{C}-V_{0}=\frac{9}{2}B\omega l^{2}\]

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Question 2: moderate

A wire forming one cycle of sine curve is moved in x-y plane with velocity

\[\overrightarrow{V}=V_{x}\hat{i}+V_{y}\hat{j}\] .
There exist a magnetic field \[\overrightarrow{B}=-B_{0}\hat{k}\] . Find
the motional emf develop across the ends PQ of wire :

1. \[\lambda V_{y}B_{0}\]

2. \[\lambda V_{x}B_{0}\]

3. \[\frac{\lambda V_{y}}{B_{0}}\]

4. None

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Question 3: easy

A copper rod AB of length L, pivoted at one end A, rotates at constant angular velocity ω, at right angles to a uniform magnetic field of induction B. The e.m.f developed between the mid point C of the rod and end B is :

1. \[\frac{B\omega l^{2}}{4}\]

2. \[\frac{B\omega l^{2}}{2}\]

3. \[\frac{3B\omega l^{2}}{4}\]

4. \[\frac{3B\omega l^{2}}{8}\]

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Question 4: moderate

The magnetic field in a region is given by

\[\overrightarrow{B}=B_{0}\left( 1+\frac{x}{a} \right)\hat{k}\]
. A square loop of edge – length d is placed with its edge along x & y axis. The loop is moved with constant velocity \[\overrightarrow{V}=V_{0}\hat{i}\]. The emf induced in the loop is

1. \[\frac{V_{0}B_{0}d^{2}}{a}\]

2. \[\frac{V_{0}B_{0}d^{2}}{2a}\]

3. \[\frac{V_{0}B_{0}a^{2}}{d}\]

4. None

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Question 5: difficult

A metal disc rotates freely, between the poles of a magnet in the direction indicated. Brushes P and Q make contact with the edge of the disc and the metal axle.What current, if any, flows through R?

1. a current from P to Q

2. a current from Q to P

3. no current, because the emf in the disc is opposed by the back emf

4. no current, because the emf induced in one side of the disc is opposed by the emf induced in the other side.

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Question 6: difficult

A rectangular loop has a sliding connector PQ of length l and resistance RΩ and it is moving with a speed v as shown. The set-up is placed in a uniform magnetic field going into the plane of the paper. The three currents I1, I2 and I are

1. \[I_{1}=I_{2}=I=\frac{Blv}{R}\]

2. \[I_{1}=I_{2}=\frac{Blv}{6R}=I=\frac{Blv}{3R}\]

3. \[I_{1}=-I_{2}=\frac{Blv}{R}=I=\frac{2Blv}{3R}\]

4. \[I_{1}=I_{2}=\frac{Blv}{3R}=I=\frac{2Blv}{3R}\]

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Question 7: moderate

Select the correct alternative. A thin semicircular conducting ring of radius R is falling with its plane vertical in a horizontal magnetic induction \[\overrightarrow{B}\] . At the position MNQ the speed of the ring is v & the potential difference developed across the ring is :

1. zero

2. BvπR²/2 & M is at higher potential

3. π RBV & Q is at higher potential

4. 2 RBV & Q is at higher potential

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Question 8: difficult

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. \[V_{A}-V_{0}=\frac{B\omega l^{2}}{2}\]

2. \[V_{0}-V_{C}=\frac{9}{2}B\omega l^{2}\]

3. \[V_{A}-V_{C}=8B\omega l^{2}\]

4. \[V_{C}-V_{0}=\frac{9}{2}B\omega l^{2}\]

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Question 9: easy

A conducting rod is moved with a constant velocity v in a magnetic field. A potential difference appears across the two ends

1. \[if \overrightarrow{v} \parallel \overrightarrow{l}\]

2. \[if \overrightarrow{v} \parallel \overrightarrow{B}\]

3. \[if \overrightarrow{l} \parallel \overrightarrow{B}\]

4. none of these

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Question 10: moderate

A square metal loop of side 10 cm and resistance 1 Ω is moved with a constant velocity partly inside a magnetic field of 2 Wbm–², directed into the paper, as shown in the figure. This loop is connected to a network of five resistors each of value 3 Ω. If a steady current of 1 mA flows in the loop, then the speed of the loop is :

1. \[0.5 cms^{-1}\]

2. \[1 cms^{-1}\]

3. \[2 cms^{-1}\]

4. \[4 cms^{-1}\]

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