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Q. No.A long solenoid of length L, having turns N and of radius of cross-section R has a single circular wire wound around it tightly, making a single turn. A current i=Iosinωt is passed through this outer wire. The peak EMF induced across the ends of the inner solenoid is (nearly), in magnitude,
1.
πμ0R2N2ωI0L
2.
μ0R2ωI0NL
3.
πμ0L2NωI0R
4.
πμ0R2NωI0L
Subtopic: Self - Inductance |
50%
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Two identical conducting rods OP,OQ of length l each, rotate about O in the plane, as shown, with angular velocities ω1, ω2. There is a uniform magnetic field B acting into the plane. The magnitude of the potential difference (VP−VQ) is:
| 1. | 12B(ω1−ω2)l2 |
| 2. | B(ω1−ω2)l2 |
| 3. | 12B(ω1+ω2)l2 |
| 4. | B(ω1+ω2)l2 |
Subtopic: Motional emf |
56%
From NCERT
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A circular ring is falling in a vertical plane, in a uniform horizontal magnetic field (B) which passes perpendicular to the plane of the ring. P is the highest point, while S is the left-most point of the ring. The potential difference between P and S is (when the speed of the ring is v):
| 1. | Zero |
| 2. | √2Brv |
| 3. | πr2Bv4 |
| 4. | Brv |
Subtopic: Motional emf |
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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∘ with its length. The emf induced in the rod is:
| 1. | vBl | 2. | vBl2 |
| 3. | √32vBl | 4. | 1√3vBl |
Subtopic: Motional emf |
73%
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An inductor (L) and a capacitor (C) are connected in a circuit, with the capacitor initially charged to a maximum voltage V0. The switch is now closed. The maximum current in the circuit is:
| 1. | V0√LC | 2. | V0√LC |
| 3. | V0√LC | 4. | V0√CL |
Subtopic: Self - Inductance |
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An inductor (L) and a resistor (R) are connected in series across a battery of emf E, and the circuit is switched on. The current rises steadily. The rate of increase of the current (i.e.,didt), when the voltage drops across the resistor is E2, is given by: didt =
| 1. | EL | 2. | E2L |
| 3. | 2EL | 4. | ELe−1 |
Subtopic: LR circuit |
84%
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A horizontal square loop of area A has n turns of wire. It is immersed in a uniform, rotating magnetic field B which is initially perpendicular to the plane of the loop. The field rotates with an angular speed ω about a diagonal of the loop. The EMF induced across the loop is:
| 1. | constant, of magnitude nωBA. |
| 2. | increasing with time t, of magnitude nω2BAt. |
| 3. | decreasing with time t, of magnitude nBAt. |
| 4. | sinusoidal with time t, of amplitude nωBA. |
Subtopic: Motional emf |
58%
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The mutual inductance between the two circuits can be determined by simply letting a current i flow through one circuit and finding the flux of the magnetic field through the second circuit: ϕ2=M12i1, where M12 is the mutual inductance. Using this method, or otherwise determine the mutual inductance (M) between a long straight wire, and a small coplanar loop of the area A, located at a distance l from the wire. The value of M is:
| 1. | μ0l2π | 2. | μ0A2πl |
| 3. | μ0l34πA | 4. | μ0A22πl3 |
Subtopic: Mutual Inductance |
80%
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A metallic rod of length 3 m rotates with an angular speed of 4 rad/s in a uniform magnetic field. The field makes an angle of 30∘ with the plane of rotation. The emf induced across the rod is 72 mV. The magnitude of the field is:
1. 4×10−3 T
2. 8×10−3 T
3. 16×10−3 T
4. 48×10−3 T
1. 4×10−3 T
2. 8×10−3 T
3. 16×10−3 T
4. 48×10−3 T
Subtopic: Motional emf |
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A square wire loop of resistance 0.5 Ω/m, having a side 10 cm and made of 100 turns is suddenly flipped in a magnetic field B, which is perpendicular to the plane of the loop. A charge of 2×10−4 C passes through the loop. The magnetic field B has the magnitude of:
1. 2×10−6 T
2. 4×10−6 T
3. 2×10−3 T
4. 4×10−3 T
1. 2×10−6 T
2. 4×10−6 T
3. 2×10−3 T
4. 4×10−3 T
Subtopic: Magnetic Flux |
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