Q. No.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.
\(\dfrac{5\mu_{0} I}{6}\)
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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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| 1. | \(B\) | 2. | \(3B\) |
| 3. | \(\dfrac {B} {\sqrt3}\) | 4. | \(\sqrt 3~ B\) |
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| 1. | \(\theta=\dfrac{\pi}{3}\) | 2. | \(\theta=\dfrac{\pi}{2}\) |
| 3. | \(\theta=1\) rad | 4. | \(\theta=2\) rad |
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Then,
| 1. | \(OP=R\) | 2. | \(OP=\dfrac R2\) |
| 3. | \(OP=\sqrt3R\) | 4. | \(OP=8R\) |
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| 1. | \({\Large\frac{\mu_0i}{4R}}\) |
| 2. | \({\Large\frac{\mu_0i}{4R}}+{\Large\frac{\mu_0i}{2\pi R}}\) |
| 3. | \({\Large\Big(\frac{\mu_0i}{4R}+\frac{\mu_0i}{4\pi R}\Big)} \) |
| 4. | \({\Large\Big[\Big(\frac{\mu_0i}{4R}\Big)^2+\Big(\frac{\mu_0i}{2\pi R}\Big)^2\Big]^{1/2}} \) |
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| 1. | \(\dfrac{K}{a}\) | 2. | \(\dfrac{K}{b}\) |
| 3. | \(\dfrac{K}{a-b}\) | 4. | \(\dfrac{K}{a+b}\) |
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| 1. | \(\dfrac{\mu_0i}{4r}\) |
| 2. | \(\dfrac{\mu_0i}{4r}+\dfrac{\mu_0i}{2\pi r}\) |
| 3. | \(\dfrac{\mu_0i}{4r}+\dfrac{\mu_0i}{4\pi r}\) |
| 4. | \(\left[\left(\dfrac{\mu_0i}{4r}\right)^2+\left(\dfrac{\mu_0i}{4\pi r}\right)^2\right]^{\frac12} \) |
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| 1. | \(\dfrac{\mu_0~L~r~i}{V}\) | 2. | \(\dfrac{\mu_0~L~r~i}{2\pi~V}\) |
| 3. | \(\dfrac{\mu_0~L~r~i}{2V}\) | 4. | \(\dfrac{\mu_0~L~r~i}{4\pi~V}\) |
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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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