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Q. No.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
Subtopic: Magnetic Field due to various cases |
73%
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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 |
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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%
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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%
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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%
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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 |
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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%
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Two long straight wires carrying currents \(i_1, i_2\) are placed as shown in the figure, just avoiding contact. The separation between the wires is negligible, and the wires are aligned along \(x\) & \(y\) axes respectively.
The wire along the \(x\text-\)axis experiences:
The wire along the \(x\text-\)axis experiences:
| 1. | a force along \(+y\) axis only. |
| 2. | a force along \(-y\) axis. |
| 3. | zero force, but a torque. |
| 4. | no force and no torque. |
Subtopic: Force between Current Carrying Wires |
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A current \(i\) is distributed uniformly over the cross-section of a cylindrical wire of radius \(R,\) as shown in the diagram. The magnetic field at the surface is \(B_s.\) The magnetic field at the point \(P\) inside the cross-section equals: \(\left(OP =\dfrac{R}{2}\right )\)
| 1. | \(\dfrac{B_s}{2}\) | 2. | \(2 B_s\) |
| 3. | \(\dfrac{B_s}{4}\) | 4. | \(4 B_s\) |
Subtopic: Ampere Circuital Law |
57%
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Two semi-circular current-carrying wires are placed in the same plane so that they share a common centre. The magnetic field due to any one of them at the common centre has the magnitude, \(B_O\). When one of them is tilted so that it is in a perpendicular plane, with the same centre, the magnetic field at the common centre is \(B\). Then,
1. \(B =2B_O\)
2. \(B~=\dfrac{B_O}{2}\)
3. \(B=\sqrt 2 B_O\)
4. \(B=\dfrac{B_O}{\sqrt 2}\)
1. \(B =2B_O\)
2. \(B~=\dfrac{B_O}{2}\)
3. \(B=\sqrt 2 B_O\)
4. \(B=\dfrac{B_O}{\sqrt 2}\)
Subtopic: Magnetic Field due to various cases |
74%
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