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Q. No.In a cyclotron, a charged particle
1. undergoes acceleration all the time.
2. speeds up between the dees because of the magnetic field.
3. speeds up in a dee.
4. slows down within a dee and speeds up between dees.
Level 3: 35%-60%
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A toroid of \(n\) turns, mean radius \(R\) and cross-sectional radius \(a\) carries current \(I\). It is placed on a horizontal table taken as \(x-y\) plane. Its magnetic moment \(m\)
1. is non-zero and points in the \(z\)-direction by symmetry.
2. points along the axis of the tortoid \(( {m}=m \hat{{\phi}}).\)
3. is zero, otherwise there would be a field falling as \(\frac{1}{r^3}\) at large distances outside the toroid.
4. is pointing radially outwards.
1. is non-zero and points in the \(z\)-direction by symmetry.
2. points along the axis of the tortoid \(( {m}=m \hat{{\phi}}).\)
3. is zero, otherwise there would be a field falling as \(\frac{1}{r^3}\) at large distances outside the toroid.
4. is pointing radially outwards.
Subtopic: Magnetic Moment |
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Level 3: 35%-60%
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Consider the two idealized systems: (i) a parallel plate capacitor with large plates and small separation and (ii) a long solenoid of length \(L >>R\), radius of cross-section. In (i) \({E}\) is ideally treated as a constant between plates and zero outside. In (ii) magnetic field is constant inside the solenoid and zero outside. These idealised assumptions, however, contradict fundamental laws as below:
1. case (i) contradicts Gauss's law for electrostatic fields.
2. case (ii) contradicts Gauss's law for magnetic fields.
3. case (i) agrees with \(\oint {E} \cdot {d} {l}=0\)
4. case (ii) contradicts \(\oint{H} \cdot {d} {l}=I_{e n}\)
1. case (i) contradicts Gauss's law for electrostatic fields.
2. case (ii) contradicts Gauss's law for magnetic fields.
3. case (i) agrees with \(\oint {E} \cdot {d} {l}=0\)
4. case (ii) contradicts \(\oint{H} \cdot {d} {l}=I_{e n}\)
Subtopic: Ampere Circuital Law |
Level 3: 35%-60%
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A charged particle would continue to move with a constant velocity in a region wherein,
| (A) | \(E=0, ~B\ne0\) |
| (B) | \(E\ne0, ~B\ne0\) |
| (C) | \(E\ne0, ~B=0\) |
| (D) | \(E=0, ~B=0\) |
Choose the correct option:
1. (A), (C)
2. (B), (D)
3. (B), (C), (D)
4. (C), (D)
Subtopic: Lorentz Force |
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Level 3: 35%-60%
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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)
Subtopic: Lorentz Force |
Level 3: 35%-60%
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Two identical current-carrying coaxial loops carry current \(I\) in an opposite sense. A simple amperian loop passes through both of them once. Calling the loop as \(C,\)
| (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) |
Subtopic: Ampere Circuital Law |
Level 3: 35%-60%
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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)
Subtopic: Lorentz Force |
Level 3: 35%-60%
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The gyro-magnetic ratio of an electron in an H-atom, according to the Bohr model, is:
| 1. | independent of which orbit it is in. |
| 2. | negative. |
| 3. | positive. |
| 4. | increases with the quantum number \(n\). |
Subtopic: Magnetic Moment |
58%
Level 3: 35%-60%
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An electron is projected with uniform velocity along the axis of a current-carrying long solenoid. Which of the following is true?
| 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. |
Subtopic: Lorentz Force |
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Level 2: 60%+
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A current-carrying circular loop of radius R is placed in the x-y plane with center at the origin. Half of the loop with x > 0 is now bent so that it now lies in the y-z plane.
| 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. |
Subtopic: Magnetic Moment |
Level 3: 35%-60%
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