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: 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 4: 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 5: 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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Question 6: moderate

A wheel with ten metallic spockes each 0.50 m long is rotated with a speed of 120 rev/min in a plane normal to the earth’s magnetic field at the place. If the magnitude of the field is 0.4 Gauss, the induced e.m.f. between the axle and the rim of the wheel is equal to :

1. \[1.256\times 10^{-3} V\]

2. \[6.28\times 10^{-4} V\]

3. \[1.256\times 10^{-4} V\]

4. \[6.28\times 10^{-5} V\]

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Using the formula for induced e.m.f. in a rotating conductor:

e = \frac{1}{2} B \omega L^2 = \frac{1}{2} B (2\pi f) L^2

Substituting

e = \frac{1}{2} \times (0.4 \times 10^{-4}) \times (4\pi) \times (0.5)^2 = 6.28 \times 10^{-5}\text{ V}

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