In what direction would a B field have to point for a beam of electrons moving to the right to go undeflected through a region where there is a uniform electric field pointing vertically upward? Explain.

For the electron beam to pass through the field without deviating, the electric and magnetic force must be of the same magnitude and in the opposite direction.

In this case the electric force is

[tex]F_{e}[/tex] = q E

Where the burden of proof is considered positive.

As in the electric field it points vertically upwards, the force for a negative charge electron charge is directed vertically downwards.

To compensate for this force the magnetic force must go vertically upwards, we use the expression

[tex]F_{m}[/tex] = q v x B

And the rule of the right hand, the thumb points in the direction of the speed, the fingers extended in the direction of the magnetic field and the palm is in the direction of the electric force, this for a positive test charge

Let's apply in our case, the thumb points to the right, the palm must be vertical for a positive charge, in this case the reader is a negative charge, so palm points down, the extended fingers are in the Horizontal direction coming out of the page; this is the direction of the magnetic field