Ncert Exercises & Solutions

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)

(3) Hint: Find the Lorentz force on the particles.

Step 1: The magnetic force, F=q(vxB) on charge particle is either zero or F is perpendicular to v (or component of v) which in turn revolves particles on a circular path with uniform speed. In both cases, the particles have equal accelerations due to magnetic force.

Step 2: Both the particles gain or lose energy at the same rate as both are subjected to the same electric force (F = qE) in opposite direction.

Step 3: Since there is no change in the Centre of Mass (CM) of the particles, therefore the motion of the Centre of Mass (CM) is determined by B alone.

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