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Two current carrying loops of wire are placed as shown in the figure, the inner loop \((P)\) having a radius \((r)\) which is much smaller than the radius \((R)\) of the outer loop \((Q)\). Both the loops are concentric, but the currents in one case are in the same sense while in the other, in the opposite sense.
In both cases, the torque on \(P\) due to \(Q\) is zero. If \(P\) is slightly rotated about a diameter, then, it will return to its initial position in:
1.
case (I) but not in case (II).
2.
case (II) but not in case (I).
3.
both cases (I) and (II).
4.
neither of cases (I) and (II).
Subtopic: Â Magnetic Moment |
 52%
Level 3: 35%-60%
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A particle of mass \(m\) and the charge \(q\) is observed to move with a uniform velocity \(v\) in a region containing a uniform magnetic field \(B,\) and a uniform gravitational field \(g.\) The magnetic field \(B\) must satisfy:
| 1. | \(B = \dfrac{mg}{qv}\) | 2. | \(B \leq \dfrac{m g}{q v}\) |
| 3. | \(B \geq \dfrac{m g}{q v}\) | 4. | \(B = \dfrac{qv}{mg}\) |
Subtopic: Â Lorentz Force |
Level 3: 35%-60%
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A straight current-carrying wire carrying current \(I\) passes perpendicular to the plane of an imaginary rectangular loop \(PQRS\), passing through its centre \(O\) (into the diagram). The diagonals intersect at \(60^\circ,\) and side \(PS\) is smaller than side \(PQ. \) The value of \(\int \vec{B} \cdot d\vec{l} \) evaluated from \(P \) to \(Q \) (along \(PQ \)) has the magnitude:
| 1. | \(\dfrac{\mu_{0} I}{6}\) | 2. | \(\dfrac{2 \mu_{0} I}{6}\) |
| 3. | \(\dfrac{4\mu_{0} I}{6}\) | 4. | \(\dfrac{5\mu_{0} I}{6}\) |
Subtopic: Â Ampere Circuital Law |
 52%
Level 3: 35%-60%
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Two particles of equal mass \(m\) and charge \(q\) move in a circular orbit of radius \(r\) under the influence of a magnetic field \(B.\) The kinetic energy of the particles is proportional to (assume that the particles don't exert electrostatic forces on each other):
| 1. | \(q^{2}\) | 2. | \(B^{2}\) |
| 3. | \(r^{2}\) | 4. | All of the above |
Subtopic: Â Lorentz Force |
 90%
Level 1: 80%+
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The magnetic field at a point (\(P\)) on the axis of a circular current-carrying wire is \(\dfrac18\) of the field at its centre. The radius of the circular curve is \(R.\) The distance between \(P\) and the centre of the circle \((OP)\) is:
Then:
Then:
| 1. | \(OP=R\) | 2. | \(OP=\dfrac R2\) |
| 3. | \(OP=\sqrt3R \) | 4. | \(OP=8R\) |
Subtopic: Â Magnetic Field due to various cases |
 75%
Level 2: 60%+
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A long solenoid has a square cross-section of side \(a\). It has turn-density n (number of turns per unit axial length). A current \(i\) is passed through this solenoid. The magnetic field at the centre of the solenoid is \(B_c\). Then, \(B_c\) is proportional to:
(I) \(a\)
(II) \( \dfrac{1} {a}\)
(III) \(n\)
(IV) \(i\)
Choose the correct option from the given ones:
1. I, III, IV
2. II, III, IV
3. III, IV
4. IV Only
(I) \(a\)
(II) \( \dfrac{1} {a}\)
(III) \(n\)
(IV) \(i\)
Choose the correct option from the given ones:
1. I, III, IV
2. II, III, IV
3. III, IV
4. IV Only
Subtopic: Â Magnetic Field due to various cases |
 72%
Level 2: 60%+
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A current \(i\) flows through a semi-circular loop of radius \(r,\) attached to two long straight wires along the open diameter of the loop. The magnetic field at the centre of the loop is:
| 1. | \(\dfrac{\mu_0i}{4r}\) |
| 2. | \(\dfrac{\mu_0i}{4r}+\dfrac{\mu_0i}{2\pi r}\) |
| 3. | \(\dfrac{\mu_0i}{4r}+\dfrac{\mu_0i}{4\pi r}\) |
| 4. | \(\left[\left(\dfrac{\mu_0i}{4r}\right)^2+\left(\dfrac{\mu_0i}{4\pi r}\right)^2\right]^{\frac12} \) |
Subtopic: Â Magnetic Field due to various cases |
 84%
Level 1: 80%+
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A charged particle moves in a circular path of radius \(r\) in a uniform magnetic field \(B,\) perpendicular to the plane of motion. The same particle is observed to move in a circular path around an infinite line charge \(\lambda\) (charge/unit length), moving with the same kinetic energy as before. The charge to mass ratio of the particle is proportional to:
| 1. | \(\lambda Br\) | 2. | \(\dfrac{\lambda Br}{r}\) |
| 3. | \(\dfrac{\lambda}{Br}\) | 4. | \(\dfrac{\lambda}{B^2r^2}\) |
Subtopic: Â Lorentz Force |
Level 3: 35%-60%
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A galvanometer \(G\) (having very small resistance), when connected with a resistance of \(10~\text k\Omega\) in series, can function as a voltmeter measuring a maximum voltage of \(20\) V. The current required to give a full scale deflection on the galvanometer is:
1. \(0.1\) mA
2. \(0.2\) mA
3. \(1\) mA
4. \(2\) mA
1. \(0.1\) mA
2. \(0.2\) mA
3. \(1\) mA
4. \(2\) mA
Subtopic: Â Moving Coil Galvanometer |
 79%
Level 2: 60%+
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A long solenoid of radius \(1~\text{mm}\) has \(100\) turns per mm. If \(1~\text{A}\) current flows in the solenoid, the magnetic field strength at the centre of the solenoid is:
| 1. | \(6.28 \times 10^{-4} ~\text{T} \) | 2. | \(6.28 \times 10^{-2}~\text{T}\) |
| 3. | \(12.56 \times 10^{-2}~\text{T}\) | 4. | \(12.56 \times 10^{-4} ~\text{T}\) |
Subtopic: Â Magnetic Field due to various cases |
 65%
Level 2: 60%+
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