Q. No. 
1. \(9~\text{V}\)
2. \(8.8~\text{V}\)
3. \(8~\text{V}\)
4. \(10~\text{V}\)
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A circular wire carrying current \(I\) produce the same magnetic field at its centre as an infinite straight wire carrying the same current \((I)\) does, at a distance \(d\). The radius of the circular wire is:
| 1. | \(\dfrac{d}{2\pi}\) | 2. | \(\dfrac{d}{\pi}\) |
| 3. | \(2\pi d\) | 4. | \(\pi d\) |
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A particle of mass \(m\), charge \(q\) enters a region where there is a uniform magnetic field \(B\), its initial motion being perpendicular to the field. Along the direction of the magnetic field, there is also an electric field \(E\), which is uniform. By the time the particle has turned through a "full circle" in the plane perpendicular to \(B\), its speed doubled. The initial speed is:
| 1. | \(\dfrac{E}{B}\) |
| 2. | \(\dfrac{2 \pi E}{B}\) |
| 3. | \(\dfrac{2 \pi \sqrt{3} E}{B}\) |
| 4. | \(\dfrac{2 \pi E}{\sqrt{3} B}\) |
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Two insulated current carrying wires lie along the \(x\) and the \(y\text-\)axis in the \(xy\text-\)plane, carrying identical currents \(I\). The magnetic field at the point \((d,-d)\) is:
| 1. | \(\text{Zero}\) | 2. | \(\dfrac{\mu_0I}{\pi d}\) |
| 3. | \(\sqrt2\cdot \dfrac{\mu_0I}{2\pi d}\) | 4. | \(\dfrac{\mu_0I}{2\pi (\sqrt2 d)}\) |
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| 1. | The force on the loop is \(4iaB\). |
| 2. | The torque on the loop is \(ia^2B\). |
| 3. | The force on the loop is \(\sqrt {2} iaB\). |
| 4. | The torque on the loop is \(\sqrt{2}ia^2B\). |
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| 1. | \(\dfrac{\mu_{0} i}{2 \pi d}\) | 2. | \(\dfrac{2\mu_{0} i}{2 \pi d}\) |
| 3. | \(\dfrac{\sqrt 3\mu_{0} i}{2 \pi d}\) | 4. | zero |
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When a particle of charge \(q\) and mass \(m\) is projected perpendicular to a magnetic field, it moves in a circle of radius \(r.\) When the particle is projected upward with the same kinetic energy in a uniform gravitational field \((g)\), it rises to a height \(h\). The magnetic field is:
| 1. | \(\dfrac{m}{q r} \sqrt{\dfrac{g h}{2}}\) | 2. | \(\dfrac{2m}{q r} \sqrt{\dfrac{g h}{2}}\) |
| 3. | \(\dfrac{m}{2q r} \sqrt{\dfrac{g h}{2}}\) | 4. | none of the above. |
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(I) \(a\)
(II) \( \dfrac{1} {a}\)
(III) \(n\)
(IV) \(i\)
Choose the correct option from the given ones:
1. I, III, IV
2. II, III, IV
3. III, IV
4. IV Only
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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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