Q. No.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.
\(\dfrac{\mu_{0} i^{2} L}{4 r}\)
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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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| 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. |
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