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: \(\left( \dfrac{e}{m} \right)_{1} + \left( \dfrac{e}{m} \right)_{2} = 0\)

Subtopic:  Lorentz Force |
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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.

Subtopic:  Biot-Savart Law |
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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 |
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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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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 |
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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 |
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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 are correct?
1. (a) and (b)
2. (a) and (c)
3. (b) and (c)
4. (c) and (d)

Subtopic:  Ampere Circuital Law |
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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 |
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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)

Subtopic:  Lorentz Force |
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