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Q. No.A square loop with a side length of \(10~\text{cm}\) is placed vertically in the east-west plane. A uniform magnetic field of \(0.1~\text{T}\) is applied across the plane of the loop in the northeast direction. The magnetic flux linked with the loop is:
| 1. | \(\sqrt2\times10^{-2}\) Wb | 2. | \(\sqrt2\times10^{-3}\) Wb |
| 3. | \(\dfrac{1}{\sqrt{2}}\times10^{-2}\) Wb | 4. | \(\dfrac{1}{\sqrt{2}}\times10^{-3}\) Wb |
Subtopic: Magnetic Flux |
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Level 2: 60%+
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The magnetic flux through a coil perpendicular to its plane is varying according to the relation \(\phi = (5t^3 + 4t^{2} +2t-5)~\text{Wb}.\) If the resistance of the coil is \(5~\Omega,\) then the induced current through the coil at \(t=2~\text s\) will be:
1. \(15.6~\text A\)
2. \(16.6~\text A\)
3. \(17.6~\text A\)
4. \(18.6~\text A\)
1. \(15.6~\text A\)
2. \(16.6~\text A\)
3. \(17.6~\text A\)
4. \(18.6~\text A\)
Subtopic: Faraday's Law & Lenz Law |
86%
Level 1: 80%+
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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 |
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Level 3: 35%-60%
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The self-inductance of a coil in which an emf of \(20~\text V\) is induced when the current in the circuit changes uniformly from \(1~\text A\) to \(2.5~\text A\) in \(0.5~\text s\) is:
| 1. | \(\dfrac{20}{3}~\text H\) | 2. | \(\dfrac{40}{3}~\text H\) |
| 3. | \(\dfrac{17}{3}~\text H\) | 4. | \(\dfrac{50}{3}~\text H\) |
Subtopic: Self - Inductance |
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Level 1: 80%+
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A small square loop of wire of side \(\ell \) is placed inside a large square loop of wire \(L\) \((L\gg l).\) Both loops are coplanar and their centres coincide at point \(O\) as shown in the figure. The mutual inductance of the system is:
| 1. | \(\dfrac{2\sqrt{2}\mu _{0}L^{2}}{\pi \ell}\) | 2. | \(\dfrac{\mu_{0} \ell^{2}}{2 \sqrt{2} \pi {L}} \) |
| 3. | \(\dfrac{2 \sqrt{2} \mu_{0} \ell^{2}}{\pi {L}} \) | 4. | \(\dfrac{\mu_{0} L^{2}}{2 \sqrt{2} \pi \ell}\) |
Subtopic: Mutual Inductance |
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Level 2: 60%+
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The current in the branch of a circuit shown below increases at a rate of \(3\) A/s. At the instant when the current in the wire is \(2\) A, the potential drop from \(a\) to \(b\) is:
1. \(26~\text{V}\)
2. \(14~\text{V}\)
3. \(16~\text{V}\)
4. \(6~\text{V}\)
Subtopic: LR circuit |
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Level 2: 60%+
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A circular coil of radius \(10\) cm, \(100\) turns is placed with its plane perpendicular to the horizontal component of earth's magnetic field \((=3.0\times 10^{-5}~\text{T})\). It is rotated about its vertical diameter through \(180^\circ\) in \(0.314\) s. What is the magnitude of emf induced in the coil?
| 1. | \(3\times 10^{-4}\) V | 2. | \(6\times 10^{-4}\) V |
| 3. | \(6\times 10^{-5}\) V | 4. | \(6\times 10^{-6}\) V |
Subtopic: Faraday's Law & Lenz Law |
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Level 3: 35%-60%
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Rings are rotated and translated in a uniform magnetic field as shown in the figure. Arrange the magnitude of emf induced across \(AB\):
| 1. | \(\mathrm{emf_{a}<emf_{b}<emf_{c}}\) |
| 2. | \(\mathrm{emf_{a}=emf_{b}<emf_{c}}\) |
| 3. | \(\mathrm{emf_{a}={emf}_{c}<{emf}_{b}}\) |
| 4. | \(\mathrm{emf_{a}<emf_{b}={emf}_{c}}\) |
Subtopic: Motional emf |
Level 3: 35%-60%
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A coil is wound on a cylindrical core in the form of a closely packed helix. If all the linear dimensions of the solenoid are increased by a factor of \(2,\) while keeping the number of turns per unit length constant, the self-inductance increases by a factor of:
1. \(16\)
2. \(12\)
3. \(8\)
4. \(4\)
1. \(16\)
2. \(12\)
3. \(8\)
4. \(4\)
Subtopic: Self - Inductance |
61%
Level 2: 60%+
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Two coils \(1\) and \(2\), have mutual inductance \(M\) and resistance \(R\) each. A current flow in coil \(1\), which varies with time as; \(I_1=kt^{2},\) where \(k\) is constant, \(t\) is time. The total charge that flown through coil \(2\), between \(t=0\) to \(t=\dfrac{T}{2}\) will be:
1. \(\dfrac{MkT^2}{4R}\)
2. \(\dfrac{2MkT^2}{R}\)
3. \(\dfrac{MkT^2}{2R}\)
4. Zero
1. \(\dfrac{MkT^2}{4R}\)
2. \(\dfrac{2MkT^2}{R}\)
3. \(\dfrac{MkT^2}{2R}\)
4. Zero
Subtopic: Mutual Inductance |
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Level 3: 35%-60%
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