Final answer:
Option B is incorrect because accelerations caused by magnetic forces differ for electrons and positrons due to the force being perpendicular to the velocity. Option D is also incorrect as the center of mass motion depends on electric and magnetic forces. Therefore, the correct answer is C. Both particles gain or loose energy at the same rate.
Step-by-step explanation:
The student question pertains to a scenario where an electron and a positron enter a cubical region with an electric field and a magnetic field, with opposite velocities.
The options provided include statements about the electric and magnetic forces, as well as the energy changes and the motion of the center of mass for these particles.
To address the question: Option A is correct because the electric force F = qE acts on both the electron and the positron with the same magnitude but opposite directions due to their equal but opposite charges, and this force produces identical acceleration assuming the mass of the electron and positron are equal.
Option B is incorrect because while the magnetic forces have equal magnitude due to the same charge magnitude, they are opposite in direction due to the opposite charges; however, the accelerations will differ because the electron and positron have the same mass and the force is perpendicular to the velocity for each particle resulting in circular motion with the same radius.
Option C is correct because energy is a scalar quantity and because the magnitudes of forces and accelerations are the same, the energy change rate (power) will also be the same. Option D is incorrect because the motion of the center of mass of a system depends on the net external force acting on the system, which includes both the electric and the magnetic effects.