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Q. No.A current-carrying loop of wire in the shape of a square of side \(a\) lies in the \(x\text-y\) plane. A uniform magnetic field \(B\) acts in the plane. Then:
1.
The force on the loop is \(4iaB\).
2.
The torque on the loop is \(ia^2B\).
3.
The force on the loop is \(\sqrt {2} iaB\).
4.
The torque on the loop is \(\sqrt{2}ia^2B\).
Subtopic: Lorentz Force |
61%
Level 2: 60%+
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Two long parallel wires carry currents, equal to \(i\) each, in opposite directions. The distance between the wires is \(d\). The net magnetic field, at a point which is at an equal distance \(d\) from each of the wires, is:
| 1. | \(\dfrac{\mu_{0} i}{2 \pi d}\) | 2. | \(\dfrac{2\mu_{0} i}{2 \pi d}\) |
| 3. | \(\dfrac{\sqrt 3\mu_{0} i}{2 \pi d}\) | 4. | zero |
Subtopic: Magnetic Field due to various cases |
Level 3: 35%-60%
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When a particle of charge \(q\) and mass \(m\) is projected perpendicular to a magnetic field, it moves in a circle of radius \(r.\) When the particle is projected upward with the same kinetic energy in a uniform gravitational field \((g)\), it rises to a height \(h\). The magnetic field is:
| 1. | \(\dfrac{m}{q r} \sqrt{\dfrac{g h}{2}}\) | 2. | \(\dfrac{2m}{q r} \sqrt{\dfrac{g h}{2}}\) |
| 3. | \(\dfrac{m}{2q r} \sqrt{\dfrac{g h}{2}}\) | 4. | none of the above. |
Subtopic: Lorentz Force |
73%
Level 2: 60%+
Hints
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: Magnetic Field due to various cases |
72%
Level 2: 60%+
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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:
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: Magnetic Moment |
51%
Level 3: 35%-60%
Hints
Two very long wires of length \(L\) are placed parallel to each other separated by a distance \(r(r << L)\). The wires carry equal currents \(i\). The force between the two wires is nearly:
| 1. | \(\dfrac{\mu_{0} i^{2} L}{2 \pi r}\) | 2. | \(\dfrac{\mu_{0} i^{2} L}{4 \pi r}\) |
| 3. | \(\dfrac{\mu_{0} i^{2} L}{2 r}\) | 4. | \(\dfrac{\mu_{0} i^{2} L}{4 r}\) |
Subtopic: Force between Current Carrying Wires |
83%
Level 1: 80%+
Hints
Identical cells are connected to identical square wire loops as shown in the two diagrams, and the magnetic fields are respectively \(B_1\) and \(B_2\) at the centres.
Then, we can conclude that:
1. \(B_1>0, B_2=0\)
2. \(B_1> B_2>0\)
3. \(B_2> B_1>0\)
4. \(B_1=0, B_2=0\)
Then, we can conclude that:
1. \(B_1>0, B_2=0\)
2. \(B_1> B_2>0\)
3. \(B_2> B_1>0\)
4. \(B_1=0, B_2=0\)
Subtopic: Biot-Savart Law |
57%
Level 3: 35%-60%
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An \(\alpha\)-particle and a proton of the same kinetic energy move along circular paths of radii \(r_{\alpha}\) and \(r_p\) respectively, in the same magnetic field. The ratio \((r_{\alpha} / r_p) \) equals:
| 1. | \(2\) | 2. | \( \dfrac{1} {2}\) |
| 3. | \(1\) | 4. | \(4\) |
Subtopic: Lorentz Force |
65%
Level 2: 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. \(B = \dfrac{qv}{mg}\)
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: Lorentz Force |
Level 3: 35%-60%
Hints
A straight long current-carrying wire carrying a current \(i\) is placed in a uniform magnetic field, and it is observed that the field vanishes at a point which is at a distance \(r\) from the wire. The force on the wire, per unit length, is:
| 1. | \(\dfrac{\mu_{0} i^{2}}{2 \pi r}\) | 2. | \(\dfrac{\mu_{0} i^{2}}{4 \pi r}\) |
| 3. | \(\dfrac{\sqrt{2} \mu_{0} i^{2}}{2 \pi r}\) | 4. | \( \dfrac{\mu_{0} r^{2}}{2 \pi r \sqrt{2}}\) |
Subtopic: Force between Current Carrying Wires |
76%
Level 2: 60%+
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