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Q. No.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: 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%
From NCERT
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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%
From NCERT
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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%
From NCERT
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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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A wire carrying a current \(i\) is bent into the form of an arc of a circle with center \(O\), joined smoothly to two long, straight wires at its ends. The magnetic field at the centre \(O\) is twice that due to the straight portions. The angle subtended at the centre \(O\) by the arc is:
| 1. | \(\theta=\dfrac{\pi}{3}\) | 2. | \(\theta=\dfrac{\pi}{2}\) |
| 3. | \(\theta=1\) rad | 4. | \(\theta=2\) rad |
Subtopic: Magnetic Field due to various cases |
62%
From NCERT
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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 cente of the circle \((OP).\) is:
Then,
Then,
| 1. | \(OP=R\) | 2. | \(OP=\dfrac R2\) |
| 3. | \(OP=\sqrt3R\) | 4. | \(OP=8R\) |
Subtopic: Magnetic Field due to various cases |
76%
From NCERT
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