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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 opposite face with velocity -v.

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 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 B alone.

Answers (1)

The correct options are (b, c, d).

F_{net} =qE + q(v \times B).

(i) In this case both particles are moving with same acceleration either due to the magnetic forces (F_m =q(v \times B)) being zero or the Fm is perpendicular to v (or component of v). This results in the particle moving with a uniform speed in a circular path.

(ii) Both the particle gain or loss energy at the same rate as the electric force is the same (Fe = qE) and in opposite directions due to the sign of charge.

(iii) Th emotion of the centre of mass is determined only by the magnetic field ‘B’ as no change is observed in the centre of mass (CM).

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