An electron moving in the direction of the +x-axis enters a region where both an electric and magnetic field are applied. The electron moves through the two fields undeflected (with constant velocity). If the magnetic field is in the -y direction, what is the direction of the electric field in this region?

The direction of the electric field will be along z-direction.

Explanation:

When electrons enter in a region where there is only magnetic field, then force exerted by the magnetic field will be

This force will deflect the electron in a direction perpendicular to its motion and also perpendicular to the magnetic field.

Whereas in the presence of electric field, force exerted by the electric field is

The direction is opposite to the direction of electric field.

As a result, electron deflected by magnetic field is nullified by the deflection by electric field. As a result, electron moves undeflected.

So, if the direction of the magnetic field is along y-direction, the direction of the electric field has to along z-direction.