To determine the direction of the electric force on an electron within the cube in the presence of a magnetic field, we need to apply the concept of the magnetic force acting on a moving charge.

Concept:

The magnetic force \(\vec{F}\) on a moving charge is given by the equation:

\(\vec{F} = q(\vec{v} \times \vec{B})\)

Where:

• \(q\) is the charge of the particle (negative for electrons).
• \(\vec{v}\) is the velocity of the particle.
• \(\vec{B}\) is the magnetic field.
• \(\vec{v}\) is along the positive y-axis.
• \(\vec{B}\) is along the negative z-axis.

The cross product \(\vec{v} \times \vec{B}\) is obtained using the right-hand rule, which states that if the fingers of the right hand are curled from the direction of \(\vec{v}\) to \(\vec{B}\), the thumb points in the direction of the force.

Applying the right-hand rule:

• The direction of \(\vec{v} \times \vec{B}\) is along the positive x-axis.

However, since the electron has a negative charge, the force direction is the opposite of \(\vec{v} \times \vec{B}\), which means it is along the negative x-axis.

Conclusion:

The direction of the electric force on the electron is towards the positive x direction relative to the orientation of the cube.