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Q. No.A conducting wire is bent into the form of a square \(ABCD,\) and electrical connections are established in two different ways:
The same potential difference is established between the two connected ends. Current is, however, allowed to take only a single path from the positive to the negative terminal by disconnecting the other path. Let the magnetic field at the centre in these cases be \(B_\text I,B_\text{II}.\) Then, \(\frac{B_\text I}{B_\text{II}}=\)
| (I) | at two adjacent vertices \(A,B\) |
| (II) | at two points \(A,C\) at the ends of a diagonal. |
| 1. | \(2\) | 2. | \(\dfrac12\) |
| 3. | \(\dfrac{1}{\sqrt2}\) | 4. | \(1\) |
Subtopic: Magnetic Field due to various cases |
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The path of a charged particle moving in a uniform magnetic field can be: (choose the best option)
| 1. | a circle |
| 2. | a straight line |
| 3. | a circle or a straight line |
| 4. | a circle, a straight line, or a parabola |
Subtopic: Lorentz Force |
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A current-carrying wire is placed in a uniform magnetic field and the force on the wire is measured at different angular positions of the wire, as it is rotated in the \(x-y\) plane. Initially, the wire is along the \(x\)-axis. The magnitude of the magnetic force\((F)\) is plotted as a function of the angle\((\theta)\) made by the current-carrying wire with the \(x\)-axis.
Which of the following is the possible magnetic field (in tesla)?
1. \(2\hat j\)
2. \(2\hat k\)
3. \(2\hat i+2\hat k\)
4. \(2\hat j+2\hat k\)
Which of the following is the possible magnetic field (in tesla)?
1. \(2\hat j\)
2. \(2\hat k\)
3. \(2\hat i+2\hat k\)
4. \(2\hat j+2\hat k\)
Subtopic: Magnetic Field due to various cases |
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Two long parallel wires carry currents, equal to \(i\) each, in opposite directions. The distance between the wires is \(d\). The net magnetic field, at a point which is at an equal distance \(d\) from each of the wires, is:
| 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 |
Subtopic: Magnetic Field due to various cases |
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A moving charged particle (charge: \(q\)) enters a uniform vertical magnetic field \(B\) and emerges in the opposite direction, in the same horizontal plane but displaced by a distance \(d.\) The momentum carried by the particle is:
1. \(\Large\frac{qBd}{2}\)
2. \(qBd\)
3. \(2qBd\)
4. \(\Large\frac{qBd}{4}\)
1. \(\Large\frac{qBd}{2}\)
2. \(qBd\)
3. \(2qBd\)
4. \(\Large\frac{qBd}{4}\)
Subtopic: Lorentz Force |
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The magnitude of the integral of the quantity \(\int\vec B\cdot d\vec{ l}\) around the loop \(PQR\) of the equilateral triangle is \(K.\) The field at the centre of the long solenoid is:
| 1. | \(\dfrac{K}{a}\) | 2. | \(\dfrac{K}{b}\) |
| 3. | \(\dfrac{K}{a-b}\) | 4. | \(\dfrac{K}{a+b}\) |
Subtopic: Ampere Circuital Law |
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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. | \(\dfrac{\mu_0I}{2\pi (\sqrt2 d)}\) |
Subtopic: Magnetic Field due to various cases |
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Two, very long parallel wires carry equal currents in opposite directions and are separated by a distance \(d.\) The magnetic energy density due to the field of the wires, at a point midway between them is \(u.\) The force per unit length acting between the wires is:
| 1. | \(\pi du\) | 2. | \(2\pi du\) |
| 3. | \(\Large\frac{\pi du}{2}\) | 4. | \(\Large\frac{\pi du}{4}\) |
Subtopic: Force between Current Carrying Wires |
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A charged particle (charge: \(q\)) moves in a circular orbit in a uniform magnetic field, its orbit enclosing a magnetic flux \(\Phi.\) The angular momentum of the particle is:
| 1. | \(q\Phi\) | 2. | \(\dfrac{q\Phi}{2\pi}\) |
| 3. | \(\pi q\Phi\) | 4. | \(\dfrac{q\Phi}{\pi}\) |
Subtopic: Lorentz Force |
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A long straight current-carrying wire is placed along the axis of a solenoid and it is found that the field within the solenoid at a distance of \(\dfrac r{10}\) from the wire is doubled when a current \(I\) passes through the wire and the solenoid, \(r\) being the radius of the solenoid. The number of turns per unit length of the solenoid are:
| 1. | \(\dfrac{5}{\sqrt3r}\) | 2. | \(\dfrac{5}{\sqrt3\pi r}\) |
| 3. | \(\dfrac{5}{r}\) | 4. | \(\dfrac{5}{\pi r}\) |
Subtopic: Magnetic Field due to various cases |
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