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Q. No.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: Motional emf |
84%
From NCERT
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Given below are two statements:
| Assertion (A): | If a permanent magnet, be oriented and moved along the axis of a conducting solenoid, an emf will be induced across the solenoid. |
| Reason (R): | As the permanent magnet is moved along the axis of the solenoid, oriented as mentioned, the magnetic field and thereby, the flux due to this field through the solenoid changes. This induces an emf, by Faraday's law. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
Subtopic: Faraday's Law & Lenz Law |
86%
From NCERT
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A straight wire \(AB\) of length \(L\) rotates about \(A,\) with an angular speed \(\omega.\) A constant magnetic field \(\mathbf B\) acts into the plane, as shown.
| Assertion (A): | The average induced electric field within the wire has a magnitude of \(\dfrac12B\omega L.\) |
| Reason (R): | The induced electric field is the motional EMF per unit length, and the motional EMF is \(\dfrac12B\omega L^2.\) |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
Subtopic: Motional emf |
55%
From NCERT
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Two long solenoids have the same total length and the same total number of turns, but their cross-sectional areas are different: \(A_1,A_2\) where \(A_1>A_2.\) Their self-inductances \(L_1,L_2\) are in the ratio (approximately):
| 1. | \(A_1:A_2\) | 2. | \(A^2_1:A_2^2\) |
| 3. | \(A_2:A_1\) | 4. | \(A^2_2:A_1^2\) |
Subtopic: Self - Inductance |
78%
From NCERT
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Given below are two statements:
| Statement I: | A steady magnetic field can be produced by a steady current. |
| Statement II: | A steady current can be produced in a circuit by a changing magnetic field. |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Faraday's Law & Lenz Law |
55%
From NCERT
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Match the quantities in List-I with their appropriate units in List-II.
| List-I | List-II | ||
| \((\mathrm{A})\) | inductance \(\times\) current | \((\mathrm{I})\) | V |
| \((\mathrm{B})\) | frequency \(\times\) capacitance | \((\mathrm{II})\) | Wb |
| \((\mathrm{C})\) | frequency \(\times\) magnetic flux | \((\mathrm{III})\) | \(\Omega^{-1}\) |
| \((\mathrm{D})\) | electric flux | \(\mathrm{IV}\) | V-m |
| 1. | \(\mathrm{A\text-I, B\text{-}IV, C\text-II, D\text- III}\) |
| 2. | \(\mathrm{A\text-II, B\text{-}III, C\text-I, D\text- IV}\) |
| 3. | \(\mathrm{A\text-III, B\text{-}I, C\text-II, D\text- IV}\) |
| 4. | \(\mathrm{A\text-III, B\text{-}IV, C\text-II, D\text- I}\) |
Subtopic: Self - Inductance |
69%
From NCERT
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Given below are two statements:
| Statement I: | The magnetic field due to a very long current-carrying solenoid, at its centre, is inversely proportional to the radius of the solenoid, other things remaining constant. |
| Statement II: | The magnetic energy stored in a solenoid carrying a current \(I\) is directly proportional to \(I^2.\) |
| 1. | Statement I is incorrect and Statement II is correct. |
| 2. | Both Statement I and Statement II are correct. |
| 3. | Both Statement I and Statement II are incorrect. |
| 4. | Statement I is correct and Statement II is incorrect. |
Subtopic: Self - Inductance |
58%
From NCERT
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The magnetic field, through a closed loop of conducting wire covering an area of \(100\) cm2, is \(5\times10^{-2}\) T and it is uniform and normal to the area. If the field is switched off in a time of \(10\) ms, the average EMF induced is:
| 1. | \(5\) V | 2. | \(0.5\) V |
| 3. | \(0.05\) V | 4. | \(5\times10^{-4}\) V |
Subtopic: Faraday's Law & Lenz Law |
78%
From NCERT
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Given below are two statements:
| Assertion (A): | Faraday's law of electromagnetic induction is not consistent with the law of conservation of energy. |
| Reason (R): | Lenz's law is consistent with energy conservation. |
| 1. | (A) is True but (R) is False. |
| 2. | (A) is False but (R) is True. |
| 3. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 4. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
Subtopic: Faraday's Law & Lenz Law |
67%
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. \(\dfrac{Bav}{2}\)
4. zero
1. \(Bav\)
2. \(\sqrt2Bav\)
3. \(\dfrac{Bav}{2}\)
4. zero
Subtopic: Motional emf |
57%
From NCERT
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