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Q. No.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. \(B_1=0, B_2=0\)
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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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: Ampere Circuital Law |
52%
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Two small current-carrying loops carrying currents in the clockwise direction are placed in the same plane, separated by a distance \(d\) (which is much larger than the size of the loops). The two loops:
| 1. | attract each other. |
| 2. | repel each other. |
| 3. | exert no force on each other, but exert a torque. |
| 4. | neither exert any force nor any torque on each other. |
Subtopic: Current Carrying Loop: Force & Torque |
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A long current-carrying solenoid produces a magnetic field \(B\) at its centre, \(O\). When a current-carrying wire is placed parallel to the axis of the solenoid, the field at \(O\) has the magnitude \(2B\). The field due to wire has the magnitude (at \(O\)) of:
| 1. | \(B\) | 2. | \(3B\) |
| 3. | \(\dfrac {B} {\sqrt3}\) | 4. | \(\sqrt 3~ B\) |
Subtopic: Magnetic Field due to various cases |
57%
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