Q. No.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).
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| 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. | \(\dfrac{\mu_{0} i^{2} L}{4 r}\) |
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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. \(B_1=0, B_2=0\)
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| 1. | \(2\) | 2. | \( \dfrac{1} {2}\) |
| 3. | \(1\) | 4. | \(4\) |
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1. \(B = \dfrac{mg}{qv}\)
2. \(B \leq \dfrac{m g}{q v}\)
3. \(B \geq \dfrac{m g}{q v}\)
4. \(B = \dfrac{qv}{mg}\)
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| 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. | \( \dfrac{\mu_{0} r^{2}}{2 \pi r \sqrt{2}}\) |
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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. |
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| 1. | \(\dfrac{B_s}{2}\) | 2. | \(2 B_s\) |
| 3. | \(\dfrac{B_s}{4}\) | 4. | \(4 B_s\) |
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1. \(B =2B_O\)
2. \(B~=\dfrac{B_O}{2}\)
3. \(B=\sqrt 2 B_O\)
4. \(B=\dfrac{B_O}{\sqrt 2}\)
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| 1. | \(\dfrac{\mu_{0} I}{6}\) | 2. | \(\dfrac{2 \mu_{0} I}{6}\) |
| 3. | \(\dfrac{4\mu_{0} I}{6}\) | 4. | \(\dfrac{5\mu_{0} I}{6}\) |
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