Final answer:
The magnetic field must be directed into the page (Option E) to create a force that would cancel out the electric field acting on the electron, according to the right-hand rule applied inversely for the negatively charged electron.
Step-by-step explanation:
The question involves a scenario where an electron is traveling in the positive x-direction and there is a presence of a uniform electric field in the negative y-direction. To neutralize the force on the electron, we need to apply a magnetic field. According to the right-hand rule, for an electron (which has a negative charge), the force due to the magnetic field is in the opposite direction to what you would expect for a positive charge. Therefore, to balance the electric field force acting downwards (negative y-direction), the magnetic force must be acting upwards (positive y-direction) to sum to zero. However, since electrons are negatively charged, the direction of the magnetic field necessary to exert an upward force is opposite to what the right-hand rule would suggest for a positive charge. Taking into account the electron's velocity is in the positive x-direction, the appropriate direction for the magnetic field so that it exerts the correct upward force on the negatively charged electron is into the page (Option E).