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Q. No.Two charged particles traverse identical helical paths in a completely opposite sense in a uniform magnetic field \(\overrightarrow{B}=B_0\hat{k}. \)
| 1. | They have equal \(z-\)components of momenta. |
| 2. | They must have equal charges. |
| 3. | They necessarily represent a particle-antiparticle pair. |
| 4. | The charge to mass ratio satisfy: \(\left( \dfrac{e}{m} \right)_{1} + \left( \dfrac{e}{m} \right)_{2} = 0\) |
Biot-Savart law indicates that the moving electrons (velocity \(v\)) produce a magnetic field \(B\) such that:
| 1. | \(B\perp v\). |
| 2. | \(B\parallel v\). |
| 3. | it obeys inverse cube law. |
| 4. | it is along the line joining the electron and point of observation. |
| 1. | The magnitude of the magnetic moment now diminishes. |
| 2. | The magnetic moment does not change. |
| 3. | The magnitude of B at (0, 0, z), z >>R increases. |
| 4. | The magnitude of B at (0, 0, z), z >>R is unchanged. |
| 1. | The electron will be accelerated along the axis. |
| 2. | The electron path will be circular about the axis. |
| 3. | The electron will experience a force at 45° to the axis and hence execute a helical path. |
| 4. | The electron will continue to move with uniform velocity along the axis of the solenoid. |
| 1. | independent of which orbit it is in. |
| 2. | negative. |
| 3. | positive. |
| 4. | increases with the quantum number \(n\). |
Consider a wire carrying a steady current \(I,\) placed in a uniform magnetic field \(B\) perpendicular to its length. Consider the charges inside the wire. It is known that magnetic forces do no work. This implies that,
| (a) | the motion of charges inside the conductor is unaffected by \(B\) since they do not absorb energy. |
| (b) | some charges inside the wire move to the surface as a result of \(B\). |
| (c) | if the wire moves under the influence of \(B\), no work is done by the force. |
| (d) | if the wire moves under the influence of \(B\), no work is done by the magnetic force on the ions, assumed fixed within the wire. |
Choose the correct option:
1. (b), (c)
2. (a), (d)
3. (b), (d)
4. (c), (d)
| (a) | \(\oint B\cdot dl= \mp 2\mu_0 I\) |
| (b) | the value of \(\oint B\cdot dl\) is independent of the sense of \(C\). |
| (c) | there may be a point on \(C\) where \(B\) and \(dl\) are perpendicular. |
| (d) | \(B\) vanishes everywhere on \(C\). |
Which of the above statements is correct?
| 1. | (a) and (b) | 2. | (a) and (c) |
| 3. | (b) and (c) | 4. | (c) and (d) |
A cubical region of space is filled with some uniform electric and magnetic fields. An electron enters the cube across one of its faces with velocity \(v\) and a positron enters via the opposite face with velocity \(-v\). At this instant,
| (a) | the electric forces on both the particles cause identical accelerations. |
| (b) | the magnetic forces on both the particles cause equal accelerations. |
| (c) | both particles gain or lose energy at the same rate. |
| (d) | the motion of the centre of mass (CM) is determined by \(\vec{B}\) alone. |
Choose the correct option:
1. (a), (b), (c)
2. (a), (c), (d)
3. (b), (c), (d)
4. (c), (d)
A charged particle would continue to move with a constant velocity in a region wherein,
| 1. | \(E=0, ~B\ne0\) |
| 2. | \(E\ne0, ~B\ne0\) |
| 3. | \(E\ne0, ~B=0\) |
| 4. | \(E=0, ~B=0\) |
Choose the correct option:
1. (a), (c)
2. (b), (d)
3. (b), (c), (d)
4. (c), (d)
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Q. No.
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