An electron is traveling in the positive x direction. A uniform electric field is present and oriented in the negative z direction. If a uniform magnetic field with the appropriate magnitude and direction is simultaneously generated in the region of interest, the net force on the electron can be made to have a magnitude of zero. What must the direction of the magnetic field be?

therefore the forces are in the opposite direction to the electric field direction, which indicates that it goes towards the negative side of the Z axis.

Consequently the electric force is in the positive direction of the z axis

us the direction of the magnetic field so that it cancels out the electric forces.

For the direction of the magnetic force we use the right hand rule. The thumb points in the direction of the speed, the fingers extended in the direction of the magnetic field and the palm in the direction of the Force if the charge is positive, if the charge is negative it is in the opposite direction

In this case we want the magnetic force to be directed in the negative direction of the z axis.

The charge moves in the positive direction of the x-axis

the palm must point in the negative directional of the Z axis, ie the negative charge

therefore the fingers extended points in the negative direction of the y-axis