Q. No.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: Â Motional emf |
Level 3: 35%-60%
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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 in the figure. 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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Level 1: 80%+
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A conducting rod \(AB\) of length \(l=1~\text{m}\) is moving at a velocity \(2~\text{m/s}\) making an angle \(30^\circ\) with its length. A uniform magnetic field \( B=1~\text{T}\) exists in a direction perpendicular to the plane of motion. The emf induced across the rod is:
1. \(1~\text V\)
2. \(2~\text V\)
3. \(1.5~\text V\)
4. \(\dfrac43~\text V\)
1. \(1~\text V\)
2. \(2~\text V\)
3. \(1.5~\text V\)
4. \(\dfrac43~\text V\)
Subtopic: Â Motional emf |
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Level 1: 80%+
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The wires \(\mathrm{P}_1\mathrm{Q}_1\) and \(\mathrm{P}_2\mathrm{Q}_2\) are made to slide on the rails with the same speed \(10~\text{m/s}\). If \(\mathrm{P}_1\mathrm{Q}_1\) moves towards the left and \(\mathrm{P}_2\mathrm{Q}_2\) moves towards the right, then the electric current in the \(19~\Omega\) resistor is:
1. zero
2. \(10~\text{mA}\)
3. \(0.1~\text{mA}\)
4. \(1~\text{mA}\)
Subtopic: Â Motional emf |
 74%
Level 2: 60%+
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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 |
 74%
Level 2: 60%+
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Two rectangular loops enter into a uniform magnetic field \(B\) with same velocity \(v\) as shown in the figure. \(V_A\) and \(V_B\) are induced emf in two loops respectively, then:
1. \(V_A>V_B\)
2. \(V_B>V_A\)
3. \(V_A=V_B\)
4. none of the above
1. \(V_A>V_B\)
2. \(V_B>V_A\)
3. \(V_A=V_B\)
4. none of the above
Subtopic: Â Motional emf |
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Level 2: 60%+
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A straight conductor of length \(6~\text{m},\) placed along the \(z\text-\)axis, begins to move along the positive \(x\text- \)axis with a velocity of \(5\) m/s in a magnetic field \(\vec {B}=(0.2 \hat{i}+0.1 \hat{j}) ~\text{T}.\) The induced EMF across the conductor is:
1. \(6\) V
2. \(3\) V
3. \(1\) V
4. \(5\) V
1. \(6\) V
2. \(3\) V
3. \(1\) V
4. \(5\) V
Subtopic: Â Motional emf |
 75%
Level 2: 60%+
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A conducting rod is rotated in a plane perpendicular to a uniform magnetic field with constant angular velocity. The correct graph between the induced emf \((e)\) across the rod and time \((t)\) is:
| 1. |  |
2. |  |
| 3. |  |
4. |  |
Subtopic: Â Motional emf |
 55%
Level 3: 35%-60%
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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: Â Motional emf |
 55%
Level 3: 35%-60%
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A metallic rod of length \(3~\text{m}\) rotates with an angular speed of \(4~\text{rad/s}\) in a uniform magnetic field. The field makes an angle of \(30^{\circ}\) with the plane of rotation. The emf induced across the rod is \(72~\text{mV}\). The magnitude of the field is:
1. \(4 \times 10^{-3}~\text{T}\)
2. \(8 \times 10^{-3}~\text{T}\)
3. \(16 \times 10^{-3}~\text{T}\)
4. \(48 \times 10^{-3}~\text{T}\)
1. \(4 \times 10^{-3}~\text{T}\)
2. \(8 \times 10^{-3}~\text{T}\)
3. \(16 \times 10^{-3}~\text{T}\)
4. \(48 \times 10^{-3}~\text{T}\)
Subtopic: Â Motional emf |
 51%
Level 3: 35%-60%
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