a proton moves with constant velocity in the + x direction through a region of uniform electric and magnetic fields. the magnetic field in the region is in the negative z-direction. what is the direction of the electric field in this region?

the electric force has the direction of the electric field, it must go in the direction of the negative y axis

Explanation:

Let's analyze the situation so that the proton moves with constant speed the summary of the force must be zero, so the magnitude of the electric force must be equal to the magnitude of the magnetic force, but its direction must be opposite.

To know the direction of the magnetic force we use the right-hand rule, where the thumb goes in the direction of speed positive x-axis, the other fingers extended in the direction of the magnetic field, negative z-axis, so the palm indicates the direction of the magnetic force for a positive charge, whereby the force is in the positive y-axis direction.

Since the electric force has the direction of the electric field, it must go in the direction of the negative y axis