A straight horizontal wire $$\mathrm{AB}$$ of length $$l$$ falls from rest under gravity. A uniform horizontal magnetic field $$B$$ acts perpendicular to the plane of motion of $$\mathrm{AB}$$, as shown. The induced emf across $$\mathrm{AB}$$, $$E$$, is proportional to:

1. $$B$$
2. $$l$$
3. time, $$t$$
4. all of the above
Subtopic: Â Motional emf |
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From NCERT
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A rod of length $$l$$ rotates with a 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. $$\frac{1}{2}Bl\omega ^{2}$$
3. $$Bl\omega ^{2}$$
4. $$2Bl\omega ^{2}$$

Subtopic: Â Motional emf |
Â 60%
From NCERT
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NEET 2023 - Target Batch - Aryan Raj Singh

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

 a. if $$\overrightarrow v \|\overrightarrow l$$ b. if  $$\overrightarrow v \|\overrightarrow B$$ c. if  $$\overrightarrow l \|\overrightarrow B$$ d. none of these

Choose the correct option:

 1 (a), (b) 2 (b), (c) 3 (d) only 4 (a), (d)

Subtopic: Â Motional emf |
Â 78%
From NCERT
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A wheel with $$10$$ metallic spokes each $$0.5$$ m long is rotated with a speed of $$120$$ rev/min in a plane normal to the horizontal component of earth’s magnetic field HE at a place. If $$H_E=0.4$$ G at the place, what is the induced emf between the axle and the rim of the wheel? ($$1$$ G=$$10^{-4}$$ T)
1. $$5.12\times10^{-5}$$ T
2. $$0$$
3. $$3.33\times10^{-5}$$
4. $$6.28\times10^{-5}$$

Subtopic: Â Motional emf |
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From NCERT
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An $$L$$-shaped rod $$(ABC;AB=BC=a)$$ moves in its own plane with a velocity $$v$$ parallel to $$AB.$$ There is a uniform magnetic field $$B$$ acting into the plane as shown. The emf developed between $$A,C$$ is:

1. $$Bav$$
2. $$\sqrt2Bav$$
3. $$\frac{Bav}{2}$$
4. zero
Subtopic: Â Motional emf |
Â 54%
From NCERT
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A conducting circular wire of radius $$r$$ is moving with constant velocity $$v$$ towards the right in a uniform magnetic field $$B.$$ We consider two points $$X,Y$$ such that chord $$XY$$ is perpendicular to the velocity $$v$$ and is at a distance $$x$$ from the centre $$(O)$$ of the circle. The EMF induced between $$X,Y$$ is $$\varepsilon.$$ Then, $$\varepsilon$$ is proportional to:

1. $$x$$
2. $$\sqrt{r^2-x^2}$$
3. $$r$$
4. $$x\sqrt{r^2-x^2}$$
Subtopic: Â Motional emf |
Â 72%
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A straight horizontal wire of mass $$m$$ and length $$l,$$ and having a negligible resistance can slide freely on a pair of conducting parallel rails, placed vertically. The rails are connected at the top by a capacitor $$C.$$ A uniform magnetic field $$B$$ exists in the region, perpendicular to the plane of the rails. The wire

 1 falls with uniform velocity. 2 accelerates down with acceleration less than $$g$$. 3 accelerates down with acceleration equal to  $$g$$. 4 moves down and eventually comes to rest.
Subtopic: Â Motional emf |
Â 67%
From NCERT
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A triangular wire frame, in the form of an equilateral triangle PQR moves with a uniform velocity into a region where there is a uniform magnetic field $$B$$. The edge PQ is parallel to the boundary of the region and the velocity $$v$$ is perpendicular to it. The emf($$E$$) induced within the frame is plotted as a function of time $$t,$$ starting from when the frame enters the magnetic field. $$E$$ is given by:

1. $$Bv^2t$$
2. $$2Bv^2t$$
3. $$\frac{\sqrt3}{2}Bv^2t$$
4. $$\frac{2}{\sqrt3}Bv^2t$$
Subtopic: Â Motional emf |
From NCERT
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A rod XY of length $$l$$ is placed in a uniform magnetic field $$B$$, as shown in the diagram. The rod moves with a velocity $$v$$, making an angle of $$60^\circ$$ with its length. The emf induced in the rod is:

1. $$vBl$$
2. $$vBl \over 2$$
3. $${\sqrt 3 \over 2}vBl$$
4. $${1 \over \sqrt 3}vBl$$
Subtopic: Â Motional emf |
Â 73%
From NCERT
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An emf is generated by an ac generator having $$100$$ turn coil, of loop area $$1$$ m2. The coil rotates at a speed of one revolution per second and placed in a uniform magnetic field of $$0.05$$ T perpendicular to the axis of rotation of the coil. The maximum value of emf is:
1. $$3.14$$ V
2. $$31.4$$ V
3. $$62.8$$ V
4. $$6.28$$ V