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,

For electrostatic force: 

on electron, $\overrightarrow{{\mathrm{F}}_{\mathrm{e}}}=-\mathrm{e}\overrightarrow{\mathrm{E}}$ $\Rightarrow \overrightarrow{{\mathrm{a}}_{\mathrm{e}}}=\frac{-\mathrm{e}\overrightarrow{\mathrm{E}}}{{\mathrm{m}}_{\mathrm{e}}}$

on positron, $\overrightarrow{{\mathrm{F}}_{\mathrm{p}}}=\mathrm{e}\overrightarrow{\mathrm{E}}$$\Rightarrow \overrightarrow{{\mathrm{a}}_{\mathrm{p}}}=\frac{\mathrm{e}\overrightarrow{\mathrm{E}}}{{\mathrm{m}}_{\mathrm{p}}}=\frac{\mathrm{e}\overrightarrow{\mathrm{E}}}{{\mathrm{m}}_{\mathrm{e}}}$

Acceleration caused by electrostatic force is not same for the particles.

For magnetic force:

The acceleration of the electron is given as,

$\overrightarrow{{\mathrm{a}}_{\mathrm{e}}}=\frac{-\mathrm{e}(\overrightarrow{\mathrm{v}}\times \overrightarrow{\mathrm{B}})}{\mathrm{m}}$

The acceleration of the positron is given as,

$\overrightarrow{{\mathrm{a}}_{\mathrm{p}}}=\frac{-\mathrm{e}(\overrightarrow{\mathrm{v}}\times \overrightarrow{\mathrm{B}})}{\mathrm{m}}$

Since, the accelerations are equal for both the particles, so the magnetic force on both the particles causes equal acceleration.

Since, the accelerations are equal for both the particles, so the magnetic force on both the particles causes equal acceleration.

The electrostatic force on the positron and electron pair will be zero. So, the motion of the centre of mass is determined by the magnetic field alone.