Q. No.Faraday's law of electromagnetic induction is used in the operation of:
1. metal detectors
2. jet engines
3. electromagnets
4. LEDs
1. metal detectors
2. jet engines
3. electromagnets
4. LEDs
Subtopic: Faraday's Law & Lenz Law |
Level 4: Below 35%
Hints
The two long, parallel wires shown in the diagram carry equal and opposite currents \(i\). The currents change linearly with time: \(\dfrac{di} {dt}\) = a constant = \(K\). The small circuit is situated midway between the wires and has an area \(A\). The emf induced in the small circuit is:
| 1. | zero | 2. | \(\dfrac{\mu_{0} A K}{2 \pi l}\) |
| 3. | \(\dfrac{\mu_{0} A K}{ \pi l}\) | 4. | \(\dfrac{2 \mu_{0} A K}{\pi l}\) |
Subtopic: Faraday's Law & Lenz Law |
Level 3: 35%-60%
Hints
Given below are two statements:
| Assertion (A): | Faraday's law of electromagnetic induction is a consequence of Biot-Savart's law. |
| Reason (R): | Currents cause magnetic fields and interact with magnetic flux. |
| 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 |
Level 3: 35%-60%
Hints
A rectangular conducting wire-frame having dimensions of \(a × 2a\) is bent symmetrically so that its two halves are at right-angle with respect to each other. A uniform, constant magnetic field \(B\) acts parallel to one of the bent sides, initially. The wire frame begins to rotate with a uniform angular speed \(\omega\) about the bend-line, \(PQ\). The emf induced in the loop will have the form:
1. \(2\omega Ba^2\sin\omega t\)
2. \(2\omega Ba^2\cos\omega t\)
3. \(\omega Ba^2(\cos\omega t+\sin\omega t)\)
4. \(\omega Ba^2(\cos\omega t-\sin\omega t)\)
1. \(2\omega Ba^2\sin\omega t\)
2. \(2\omega Ba^2\cos\omega t\)
3. \(\omega Ba^2(\cos\omega t+\sin\omega t)\)
4. \(\omega Ba^2(\cos\omega t-\sin\omega t)\)
Subtopic: Faraday's Law & Lenz Law |
Level 3: 35%-60%
Hints
A rectangular loop of conducting wire is bent symmetrically so that its two plane halves are inclined at right angles with respect to each other (i.e. \(\angle { PQR }=\angle S T U=90^{\circ}\)). Every segment has a length '\(a\)' \((PQ=QR=RS=...=UP=a).\) A uniform time-dependent magnetic field \(B(t)\) acts on the loop, making an angle '\(\alpha\)' with the lower half of the loop and '\(90^o - \alpha \)' with the upper half. The EMF induced in the loop is proportional to:
| 1. | \((\cos \alpha+\sin \alpha) \dfrac{d B}{d t} \) | 2. | \( (\cos \alpha-\sin \alpha) \dfrac{d B}{d t}\) |
| 3. | \((\tan \alpha+\cot \alpha) \dfrac{d B}{d t}\) | 4. | \( (\tan \alpha-\cot \alpha) \dfrac{dB}{d t}\) |
Subtopic: Faraday's Law & Lenz Law |
Level 3: 35%-60%
Hints
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 |
56%
Level 3: 35%-60%
Hints
The magnetic field in a region of space is increasing at the rate of \(10^{-3}~\text{T/s}\) along the \(z\)-axis. A \(10~\text{cm}\)-square coil of wire having \(10\) turns is placed in the \(x\)-\(y\) plane. The emf induced in the coil is:
(take resistance to be \(100~\Omega\))
(take resistance to be \(100~\Omega\))
| 1. | \(10^{-4}~\text V\) | 2. | \(10^{-6}~\text V\) |
| 3. | \(10^{-5}~\text V\) | 4. | \(10^{-2}~\text V\) |
Subtopic: Faraday's Law & Lenz Law |
60%
Level 2: 60%+
Hints
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 |
68%
Level 2: 60%+
Hints
A circular loop of radius \(R,\) enters a region of uniform magnetic field \(B\) as shown in the diagram. The field \((B)\) is perpendicular to the plane of the loop while the velocity of the loop, \(v\) is along its plane. The induced EMF:
| 1. | increases continuously. |
| 2. | decreases continuously. |
| 3. | first increases and then decreases. |
| 4. | remains constant throughout. |
Subtopic: Faraday's Law & Lenz Law |
69%
Level 2: 60%+
Hints
A rectangular loop \((ABCD)\) is placed in a magnitude field where the field in the left half of the loop decreases at the same rate as the field in the right half of the loop increases (at a constant rate): \({\Large\frac{dB_{\mathrm I}}{dt}}=-{\Large\frac{dB_{\mathrm{II}}}{dt}};\) \(B_{\mathrm {I}}\) and \(B_{\mathrm {II}}\) are both normal to the plane of the loop and acting inward. The EMF induced in the loop is:
1. clockwise
2. anticlockwise
3. zero
4. oscillatory
1. clockwise
2. anticlockwise
3. zero
4. oscillatory
Subtopic: Faraday's Law & Lenz Law |
73%
Level 2: 60%+
Hints
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